Roots

A quadratic equation is an equation of the form ax^{2} + 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:**

x^{2} + 6x + 8 = 0

x^{2} + 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 x^{2} + 6x + 8 equals to zero. Hence, -2 and -4 are the roots of the quadratic equation x^{2} + 6x + 8 = 0.

Finding Roots of Quadratic Equation

There are three methods for finding roots of a quadratic equation:

** ◾ By doing factorization**

** ◾ By completing the square **

** ◾ By using the quadratic formula**

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