Roots of Quadratic Equation
A quadratic equation is an equation of the form ax2 + bx + c=0 where a, b, and c are constants and a ≠ 0.
The values of variable x which satisfy the quadratic equation is called as Roots (also called solutions or zeros) of a Quadratic Equation.
The number of roots of a polynomial equation is equal to its degree. Hence, a quadratic equation has exactly 2 roots as the highest power of x in quadratic equation is 2.
For example:
x2 + 6x + 8 = 0
x2 + 2x + 4x + 8 = 0
x(x + 2) + 4(x + 2) = 0
(x + 2) (x + 4) = 0
x = -2 and x = -4
As you can see that putting either -2 or -4 in place of x makes the quadratic equation x2 + 6x + 8 equals to zero. Hence, -2 and -4 are the roots of the quadratic equation x2 + 6x + 8 = 0.
There are three methods for finding roots of a quadratic equation:
◾ By doing factorization
◾ By completing the square
◾ By using the quadratic formula