The discriminant calculator is an online calculator tool, which calculates the discriminant of a given quadratic equation.

For a quadratic equation ax² + bx + c = 0, where a ≠ 0, the formula of discriminant is b² – 4ac.

Discriminant is also denoted by symbol Δ

∴ Δ = b² – 4ac

The value of discriminant helps in deciphering
◾ Number of roots – whether the quadratic equation has two roots, one root or none.
◾ Type of roots - whether the roots are real and imaginary.

◾ If Δ > 0, then √Δ is real; hence we get two real and distinct roots.

◾ If Δ = 0, then √Δ is also zero; hence values of both x₁ and x₂ would be same and hence we get real and equal roots.

◾ If Δ < 0, then √Δ is imaginary number; hence we get imaginary roots.

◾ If Δ is a perfect square, then √Δ is a rational number; hence we get rational roots, else we get irrational roots.

Value of discriminant	Number of roots	Type of roots
Δ > 0	2	Real
Δ = 0	1	Real
Δ < 0	0	Imaginary

Step 1 - To use Discriminant Calculator, the first step is to convert the quadratic equation where we want to use Discriminant calculator, into Standard Form of Quadratic Equation.

The Standard form of quadratic equation is ax² + bx + c = 0

Hence, the first step is to change our quadratic equation in the standard form 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 - 10x = -16

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

x² - 10x = -16 is now equal to x² - 10x + 16= 0.

Now the quadratic equation has been successfully converted into standard form

Step 2 - Now, this is the most important step, where find value of coefficient a, b and c by comparing it with Standard Form of Quadratic Equation ax² + bx +c = 0.

For example, comparing x² - 10x + 16= 0. with ax² + bx +c = 0, we get

a = 1,
b = -10,
c = 16

Step 3 - Insert the values of a, b and c in formula of discriminant calculator b2 – 4ac

Hence, Discriminant, Δ = (-10)² – 4(1)(16) = 36

Since Δ > 0, hence the equation has two real and distinct roots