Quadratic formula — lesson. Maths CBSE Live product, Class 10 (2026-27).

The solution of the quadratic equation is the value of the variable that makes the equation zero. We can say these solutions as roots or zeroes.

There are three methods to solve the quadratic equations.

How quadratic formula comes?

Consider the quadratic equation \(ax^2 + bx + c = 0\), where \(a \ne 0\).

Let us find the roots of this equation by the method of completing the square.

Divide the equation by \(a\).

x^{2} + \frac{b}{a} x + \frac{c}{a} = 0

Move the constant to the right side.

x^{2} + \frac{b}{a} x = - \frac{c}{a}

Add the square of one half of coefficient of \(x\) on both sides.

x^{2} + \frac{b}{a} x + {(\frac{b}{2 a})}^{2} = - \frac{c}{a} + {(\frac{b}{2 a})}^{2}

{(x + \frac{b}{2 a})}^{2} = - \frac{c}{a} + \frac{b^{2}}{4 a^{2}}

{(x + \frac{b}{2 a})}^{2} = \frac{b^{2} - 4 ac}{4 a^{2}}

Taking square root on both sides.

x + \frac{b}{2 a} = \pm \sqrt{\frac{b^{2} - 4 ac}{4 a^{2}}}

x + \frac{b}{2 a} = \pm \frac{\sqrt{b^{2} - 4 ac}}{2 a}

x = - \frac{b}{2 a} \pm \frac{\sqrt{b^{2} - 4 ac}}{2 a}

x = \frac{- b \pm \sqrt{b^{2} - 4 ac}}{2 a}

Therefore, the roots of \(ax^2 + bx + c = 0\) are

x = \frac{- b + \sqrt{b^{2} - 4 ac}}{2 a}

and

x = \frac{- b - \sqrt{b^{2} - 4 ac}}{2 a}

The formula for finding the roots of the quadratic equation \(ax^2 + bx + c = 0\) is:

x = \frac{- b \pm \sqrt{b^{2} - 4 ac}}{2 a}

This formula is known as the quadratic formula.

Did you find an error?

1. Quadratic formula