Algebra involves solving quadratic equations . Quadratic equation is a second degree polynomial. It helps in solving may real world situations. Quadratic curves are known as circle, ellipse and hyperbola. Quadratic equation helps in solving problems on physics.
The general form of quadratic equation is ax2 + bx + x = 0 where a,b,c are real numbers.
The highest power of the variable that occurs in the equation is the degree of the equation. The value of the variable for which the value of quadratic equation becomes zero is the zero of a quadratic equation. The roots of quadratic equation are also called as zeros of quadratic equation.
The following examples illustrate finding roots of quadratic equation.
Example 1:- Find roots of quadratic equation
X^2 + 5x = 6 =0
Solution 1: -
x2 + 5x = 6 =0
( x + 2) ( x + 3 ) = 0 by factorization either x+2 = 0 or x +3 = 0
x = -2 or x = -3
Solve: (x+3)/(x+2) = (3x-7)/(2x-3)
( x+ 3) (2x – 3) = (x+2) (3x – 7) by cross multiplication
2 x2 – 3x + 6x – 9 = 3x2 – 7 x + 6x – 14
-x2 + 4x + 5 = 0
x2 - 4x - 5 = 0
(x-5) (x+ 1) =0 ( by factorization)
either x-5 = 0 or x + 1 = 0
x = 5 or x = -1
Hence, obtained the value of x.
The nature of roots can be determined by using the values of x.