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

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