# Roots of Quadratic Equation Calculator

## What are the Roots of Quadratic Equation Calculator?

'Cuemath's Roots of Quadratic Equation Calculator' is an online tool that helps to calculate the roots of a given quadratic equation. Cuemath's online Roots of Quadratic Equation calculator helps you to calculate the roots of a given quadratic equation in a few seconds.

NOTE: The coefficient of x2 should not be zero.

## How to Use Roots of Quadratic Equation Calculator?

Please follow the steps below to find the roots of the quadratic equation:

• Step 1: Enter the coefficients of a quadratic equation.
• Step 2: Click on the "Solve" button to find the roots of a given quadratic equation.
• Step 3: Click on the "Reset" button to clear the fields and find the roots for different quadratic equations.

## How to Find Roots of Quadratic Equation?

The word "Quadratic" is derived from the word "Quad" which means square. In other words, a quadratic equation is an “equation of degree 2”

An equation of the form ax+ bx + c = 0, where a≠0 is called a quadratic equation and a, b, c are coefficients of the quadratic equation.

To find the roots of a given quadratic equation, we use the discriminant formula  given by  $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

### Solved Example:

Find the roots of given quadratic equation x2 + 5x + 6 =0

### Solution:

Given: a = 1, b = 5, c = 6

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

$$x = {-5 \pm \sqrt{5^2-24} \over 2}$$

$$x = {-4 \over 2}, {-6 \over 2}$$

$$x= {-2},{-3}$$

Thereofore, roots of given quadratic equation are -2, -3

Similarly, you can try the calculator to find the roots of given quadratic equation for the following:

a)  2x2 + x − 3 = 0

b)  x2 + 10x − 11 = 0