# 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.

## What are the Roots of Quadratic Equation Calculator?

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 x^{2} 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 ^{2 }+ 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 x^{2} + 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) 2x^{2} + x − 3 = 0

b) x^{2} + 10x − 11 = 0