Hướng dẫn quadratic equation 2 php - phương trình bậc hai 2 php

Hình thức tiêu chuẩn của phương trình bậc hai là:

Các giải pháp của phương trình bậc hai này được đưa ra bởi:

Mã nguồn

Đầu ra

Chúng tôi đã nhập mô -đun <?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 1 để thực hiện căn bậc hai phức tạp. Đầu tiên, chúng tôi tính toán phân biệt đối xử và sau đó tìm hai giải pháp của phương trình bậc hai.

Bạn có thể thay đổi giá trị của A, B và C trong chương trình trên và kiểm tra chương trình này.

Đưa ra một phương trình bậc hai, nhiệm vụ là giải phương trình hoặc tìm ra rễ của phương trình. Dạng tiêu chuẩn của phương trình bậc hai là -

Examples:

Phương pháp 1: Sử dụng công thức trực tiếp Using the direct formula

Sử dụng công thức bậc hai dưới đây, chúng ta có thể tìm thấy gốc của phương trình bậc hai.

Có những trường hợp quan trọng sau đây.

<?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 6 <?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 7

<?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 8 <?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 9

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 0Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 1Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 3Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 4 Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 3__

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 0# Python program to find roots of quadratic equation import math # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c # checking condition for dcriminant if d > 0: print("Your equation has real and different roots:") print((-b + math.sqrt(d))/(2 * a)) print((-b - math.sqrt(d))/(2 * a)) elif d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is less than 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", math.sqrt(-d),'i') print(- b / (2 * a), " -", math.sqrt(-d),'i') equationroots() 3Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 # Python program to find roots of quadratic equation import math # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c # checking condition for dcriminant if d > 0: print("Your equation has real and different roots:") print((-b + math.sqrt(d))/(2 * a)) print((-b - math.sqrt(d))/(2 * a)) elif d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is less than 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", math.sqrt(-d),'i') print(- b / (2 * a), " -", math.sqrt(-d),'i') equationroots() 5# Python program to find roots of quadratic equation import math # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c # checking condition for dcriminant if d > 0: print("Your equation has real and different roots:") print((-b + math.sqrt(d))/(2 * a)) print((-b - math.sqrt(d))/(2 * a)) elif d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is less than 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", math.sqrt(-d),'i') print(- b / (2 * a), " -", math.sqrt(-d),'i') equationroots() 6# Python program to find roots of quadratic equation import math # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c # checking condition for dcriminant if d > 0: print("Your equation has real and different roots:") print((-b + math.sqrt(d))/(2 * a)) print((-b - math.sqrt(d))/(2 * a)) elif d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is less than 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", math.sqrt(-d),'i') print(- b / (2 * a), " -", math.sqrt(-d),'i') equationroots() 7

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 0# Python program to find roots of quadratic equation import math # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c # checking condition for dcriminant if d > 0: print("Your equation has real and different roots:") print((-b + math.sqrt(d))/(2 * a)) print((-b - math.sqrt(d))/(2 * a)) elif d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is less than 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", math.sqrt(-d),'i') print(- b / (2 * a), " -", math.sqrt(-d),'i') equationroots() 9 # Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 0<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 6# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 2

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 3# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 5# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 6# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 7

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 3# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4ax2 + bx + c = 0, where a, b and c are real numbers and a ≠ 00Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 6Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 3ax2 + bx + c = 0, where a, b and c are real numbers and a ≠ 03

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 3# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4ax2 + bx + c = 0, where a, b and c are real numbers and a ≠ 00Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 6Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 3___

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 0# Solve the quadratic equation ax**2 + bx + c = 0 # import complex math module import cmath a = 1 b = 5 c = 6 # calculate the discriminant d = (b**2) - (4*a*c) # find two solutions sol1 = (-b-cmath.sqrt(d))/(2*a) sol2 = (-b+cmath.sqrt(d))/(2*a) print('The solution are {0} and {1}'.format(sol1,sol2)) 3 Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 1Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 <?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 6# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 2

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 3# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 5Enter a: 1 Enter b: 5 Enter c: 6 The solutions are (-3+0j) and (-2+0j)2# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 7

Các

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 0<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 9<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 06

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 3# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 5<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 10# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 7

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 3# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 55____36

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 3# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 55____36

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 9Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 <?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 38

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 3Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 <?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 41

<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 42Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 6<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 45

# Python program to find roots of quadratic equation import math # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c # checking condition for dcriminant if d > 0: print("Your equation has real and different roots:") print((-b + math.sqrt(d))/(2 * a)) print((-b - math.sqrt(d))/(2 * a)) elif d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is less than 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", math.sqrt(-d),'i') print(- b / (2 * a), " -", math.sqrt(-d),'i') equationroots() 9 Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 9Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 <?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 6# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 2

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 3# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 5<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 55# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 7

<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 9<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 06

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 0<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 60

Output:

Phương pháp 2: Sử dụng mô -đun toán học phức tạp Using the complex math module

Đầu tiên, chúng ta phải tính toán phân biệt đối xử và sau đó tìm hai giải pháp của phương trình bậc hai bằng mô -đun CMATH.

<?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 6 <?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 1

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 9Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 <?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 38

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 3Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 <?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 41

<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 42Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 6<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 45

# Python program to find roots of quadratic equation import math # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c # checking condition for dcriminant if d > 0: print("Your equation has real and different roots:") print((-b + math.sqrt(d))/(2 * a)) print((-b - math.sqrt(d))/(2 * a)) elif d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is less than 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", math.sqrt(-d),'i') print(- b / (2 * a), " -", math.sqrt(-d),'i') equationroots() 9 Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 9Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 2 <?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 6# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 2

Equation is x*x+5x+4=0 Roots are: -1, -4 Equation is x*x+4x+5=0 Roots are: -2 ± 1 i 0<?php if(isset($_POST['a'])){ $a = $_POST['a']; } if(isset($_POST['b'])){ $b = $_POST['b']; } if(isset($_POST['c'])){ $c = $_POST['c']; } $d = $b*$b - 4*$a*$c; echo $d; if($d < 0) { echo "The equation has no real solutions!"; } elseif($d = 0) { echo "x = "; echo (-$b / 2*$a); } else { echo "x1 = "; echo ((-$b + sqrt($d)) / (2*$a)); echo "<br>"; echo "x2 = "; echo ((-$b - sqrt($d)) / (2*$a)); } ?> 60

Phương pháp 2: Sử dụng mô -đun toán học phức tạp

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 5<?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 12<?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 13

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4<?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 15

# Python program to find roots of quadratic equation import cmath # function for finding roots def equationroots(): a = float(input('Enter coefficient a: ')) while a == 0: print("Coefficient a can not equal 0") a = float(input('Enter coefficient a: ')) b = float(input('Enter coefficient b: ')) c = float(input('Enter coefficient c: ')) # calculating dcriminant using formula d = b * b - 4 * a * c if d == 0: print("Your equation has real and same roots:") print(-b / (2 * a)) # when dcriminant is not equal 0 else: print("Your equation has complex roots:") print(- b / (2 * a), " +", cmath.sqrt(d)) print(- b / (2 * a), " -", cmath.sqrt(d)) equationroots() input() 4<?php function roots($a, $b, $c) { $D = $b*$b - 4*$a*$c; if ($D >= 0){ $x1 = (-$b + sqrt($D))/(2*$a); $x2 = (-$b - sqrt($D))/(2*$a); echo "Roots are: $x1, $x2 \n"; } else { $x1 = -$b/(2*$a); $x2 = sqrt(-$D)/(2*$a); echo "Roots are: $x1 ± $x2 i \n"; } } echo "Equation is x*x+5x+4=0\n"; roots(1,5,4); echo "\nEquation is x*x+4x+5=0\n"; roots(1,4,5); ?> 17

Output: