Quadratic Equation Calculator



ax2 + bx + c = 0

What is Quadratic Equation Calculator

The quadratic equation calculator is an extremely useful online calculator, which solves any given quadratic equation by using quadratic formula

We know, that for a quadratic equation ax2 + bx + c = 0, where a ≠ 0, the quadratic formula is:

Roots(x1, x2) = −b ± √   b2 − 4ac 
         2a          

After inserting values of a, b and c and solving the quadratic equation using the quadratic formula explained above, we get two values:

x1 = −b + √   b2 − 4ac 
         2a          

x2 = −b - √   b2 − 4ac 
         2a          

These two values of x – x1 and x2, which are calculated from the quadratic formula, also known as roots of quadratic equation. These two roots are the output of quadratic equation calculator

Hence, Quadratic Equation Calculator calculates roots of a Quadratic equation

Nature of roots of Quadratic Equation

If b2 – 4ac > 0, then √b2 − 4ac  is real; in this case Quadratic equation calculator provides us a solution of two real and distinct roots.

If b2 – 4ac = 0, then √b2 − 4ac  is also zero; in this case Quadratic equation calculator provides us a solution of real and equal roots.

If b2 – 4ac < 0, then √b2 − 4ac  is imaginary number; in this case Quadratic equation calculator provides us a solution of imaginary roots.

If b2 – 4ac is a perfect square, then √b2 − 4ac  is a rational number; in this case Quadratic equation calculator provides us a solution of rational roots, else Quadratic equation calculator provides us a solution of irrational roots.

How to use Quadratic equation solver

Step 1 - At the first step in using Quadratic Equation calculator , we have to rearrange the Quadratic Equation we have, into what is known as Standard Form of Quadratic Equation, which is represented as ax2 + bx + c = 0

So, Let's suppose we have to solve a quadratic equation which is currently in the form of

x2 -11x = -24

So we rearrange this equation, so that is represented in the standard form ax2 + bx + c = 0. Hence,

x2 - 11x = -24 is now equal to x2 - 11x + 24 = 0.

Now the quadratic equation has been successfully converted into standard form

Step 2 - Now, to use our Quadratic Equation calculator, we have to input coefficient a, b and c in the calculator. So our next step is to find coefficient a, b and c. So we compare our derived equation above in standard form x2 - 11x + 24= 0 with ax2 + bx +c = 0.

Hence, we get

a = 1,
b = -11,
c = 24

Step 3

Roots(x1, x2) = −b ± √   b2 − 4ac 
         2a          


x1 = −b + √   b2 − 4ac 
         2a          


=   −(-11) + √   (-11)2 − 4(1)(24)    = 8
         2(1)          


x2 = −b - √   b2 − 4ac 
         2a          


=   −(-11) - √   (-11)2 − 4(1)(24)    = 3
         2(1)          


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