# Discriminant Value Calculator for Polynomial Quadratic Equation

Calculate the discriminant value for the given coefficients of a quadratic equation.

Computing the discriminant, it is possible to distinguish whether the quadratic polynomial has two distinct real roots, one repeated real root, or non-real complex roots.

The discriminant of a quadratic polynomial, denoted by Δ is a function of the coefficients of the polynomial which provides information about properties of the polynomial roots.

For quadratic equation ax^{2} + bx + c = 0 with real coefficients a, b and c.

The discriminant of the polynomial is follows:

Δ = b^{2} - 4 ac

### Example

Let's understand how to find the find discriminant value of polynomial quadratic equation with help of following example:

Supose we wants to find the discriminant value of polynomial quadratic equation => 4x^{2} + 5x + 8 = 0.

In this equation the real coefficients are 4, 5 and 8.

The discriminant of the polynomial = Δ = ( b^{2} - 4 ac)

= 5^{2} - 4 x 4 x 8

= 25 - 4 x 32

= 25 - 128

= -103

### Definition

The discriminant is a function of the coefficients of a polynomial equation that expresses the nature of the roots of the given quadratic equation (ax^{2} + bx + c = 0). The equations can discriminate between the possible types of answer as follows:

If discriminant value is positive, we get two real solutions

If discriminant value is zero, we get one real solution

If discriminant value is negative, we get a pair of complex solutions