"Degree" can mean several things in mathematics: Show
In Algebra "Degree" is sometimes called "Order" Degree of a Polynomial (with one variable)A polynomial looks like this:
The Degree (for a polynomial with one variable, like x) is: the largest exponent of that variable. More Examples:
Names of DegreesWhen we know the degree we can also give it a name!
Example: y = 2x + 7 has a degree of 1, so it is a linear equation Example: 5w2 − 3 has a degree of 2, so it is quadratic Higher order equations are usually harder to solve:
Degree of a Polynomial with More Than One VariableWhen a polynomial has more than one variable, we need to look at each term. Terms are separated by + or - signs:
For each term:
The largest such degree is the degree of the polynomial. Example: what is the degree of this polynomial:Checking each term:
The largest degree of those is 3 (in fact two terms have a degree of 3), so the polynomial has a degree of 3 Example: what is the degree of this polynomial:4z3 + 5y2z2 + 2yz Checking each term:
The largest degree of those is 4, so the polynomial has a degree of 4 Writing it DownInstead of saying "the degree of (whatever) is 3" we write it like this: When Expression is a FractionWe can work out the degree of a rational expression (one that is in the form of a fraction) by taking the degree of the top (numerator) and subtracting the degree of the bottom (denominator). Here are three examples: ../algebra/images/degree-example.js?mode=x0 ../algebra/images/degree-example.js?mode=x1 ../algebra/images/degree-example.js?mode=xm1 Calculating Other Types of ExpressionsWarning: Advanced Ideas Ahead! We can sometimes work out the degree of an expression by dividing ...
... then do that for larger and larger values, to see where the answer is "heading". (More correctly we should work out the Limit to Infinity of ln(f(x))ln(x), but I just want to keep this simple here). Here is an example: Example: The degree of 3 + √xLet us try increasing values of x:
Looking at the table:
So the Degree is 0.5 (in other words 1/2) (Note: this agrees nicely with x½ = square root of x, see Fractional Exponents) Some Degree Values
462, 4003, 2092, 4004,463, 1108, 2093, 4005, 1109, 4006 How many solutions are there for linear equation in two variables?Further, a linear equation in two variables has infinitely many solutions. The graph of every linear equation in two variables is a straight line and every point on the graph (straight line) represents a solution of the linear equation.
How many solutions are there in linear equations in one variable?How many solutions does a linear equation in one variable have? Every linear equation in one variable has a one and unique solution.
How many solutions are there in a linear equation?A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).
What is the degree of linear equations in two variables?The degree of the linear equation is the highest power of the variable in the linear equation. The standard form linear equation of two variables is A x + B y = C , where and are coefficients of and .
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