Quadratic Formula Calculator



ax2 + bx + c = 0

What is Quadratic formula calculator

The quadratic formula calculator is an online calculator to solve a standard quadratic equation using the Quadratic Formula, which is -

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

After solving the quadratic equation using a quadratic formula calculator, 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 Quadratic Formula Calculator, are also known as roots of quadratic equation.

Hence, Quadratic Formula 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 formula calculator gives us two real and distinct roots.

If b2 – 4ac = 0, then √b2 − 4ac  is zero; in this case, Quadratic formula calculator gives us real and equal roots.

If b2 – 4ac < 0, then √b2 − 4ac  is imaginary number; in this case, Quadratic formula calculator gives us imaginary roots.

If b2 – 4ac is a perfect square, then √b2 − 4ac  is a rational number; in this case, Quadratic formula calculator gives us rational roots, else Quadratic formula calculator gives us irrational roots

How to use Quadratic formula calculator

Step 1 - To use the Quadratic formula calculator, we have to convert the Quadratic Equation to be calculated into Standard Form of Quadratic Equation, ax2 + bx + c = 0

For example, let' suppose, we have to solve a quadratic equation which is in the form, x2 - 9x = -20. So in this case, we will convert the quadratic equation into Standard Form of Quadratic Equation, ax2 + bx +c = 0

Hence, x2 - 9x = -20 in standard form would be x2 - 9x + 20 = 0

Step 2 - Now, we have to compare the derived quadratic equation in standard form which is x2 - 9x + 20 = 0 with Standard Form of Quadratic Equation, ax2 + bx +c = 0 and find the value of a, b and c.

For example, comparing x2 - 9x + 20 = 0 with ax2 + bx + c = 0, we get

a = 1,
b = -9,
c = 20

Step 3 - Once we have derived the value of coefficients a, b and c, then all we need is to insert these values in the quadratic formula, which is

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


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


=   −(-9) + √   (-9)2 − 4(1)(20)    = 5
         2(1)          


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


=   −(-9) - √   (-9)2 − 4(1)(20)    = 4
         2(1)          


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