Got Feedback?

Found a bug? Have a suggestion? Fill the form below and we'll take a look!

X

# Discriminant Calculator

The Discriminant tells about the nature of the roots of quadratic equation. In quadratic equation formula, we have $$b^2 - 4ac$$ under root, this is discriminant of quadratic equations.
There are three cases for discriminant:
if $$b^2 - 4ac = 0$$, then the roots of quadratic equations are real and equal.
if $$b^2 - 4ac > 0$$, then the roots are real but not equal
if $$b^2 - 4ac < 0$$, then the roots are not equal and are imaginary.

$$a x^2 + bx + c = 0$$

## What is Discriminant?

Discriminant in math, is a function of coefficients of a polynomial equation. Answers of Discriminant expression can be identified as following:

if $$b^2 – 4ac = 0$$, then we get one real solution.
if $$b^2 – 4ac > 0$$, then we get two real solutions.
if $$b^2 – 4ac < 0$$, then we get two imaginary solutions.

## Discriminant Formula:

Formula for finding discriminant is:

= $$b^2 – 4ac$$

Where:

a is the coefficient of x2.

b is the coefficient of x.

c is a constant term.

Results of this formula, tells us how many solutions our quadratic has.

## Example of discriminant calculation:

### Example 1:

$$x^2 + 6x + 8 = 0$$

A = 1
B = 6
C = 8

Discriminant:
= $$b^2 – 4ac$$
= $$6^2 – 4(1)(8)$$
= $$36 – 32$$
= $$4$$

The number is positive, hence both roots of this equation are real and unequal.

### Example 2:

X2 + 4x + 12 = 0

A = 1
B = 4
C = 12

Discriminant:
= $$b^2 – 4ac$$
= $$4^2 – 4(1)(4)$$
= $$16 – 48$$
= $$-32$$

The number is negative, hence this equation has no real solution.

## What does it mean if a discriminant is positive?

If discriminant is higher than zero. It represents that the quadratic equation has two real number solutions. Graphical representation can be seen below:

## How to use Discriminant Calculator?

• Enter coefficient values for “a”, “b” and “c” in the above fields.
• Click “Submit”.
• Our discriminant calculator displays the solutions including all the steps and description at the end.

## Cases of Discriminant:

In this section, you will learn about Discriminant, how many forms of Discriminant with examples.

There are 3 cases of Discriminant.

Case 1: real and equal:

The discriminant is equal to 0 is known as real and equal.

Example:

= $$x^2 – 4x + 4$$
= $$a = 1, b = 4, c = 4$$
= $$b^2 – 4ac$$
= $$4^2 – 4(1)(2)$$
= $$16 – 16$$
= 0

The root are real and equal.

Case 2: real and unequal

The discriminant is greater then 0 is known as real and unequal.

Example:

= $$4^2 – 10x + 3$$
= $$a = 4, b = 10, c = 3$$
= $$b^2 – 4ac$$
= $$10^2 – 4(4)(3)$$
= $$100 – 48$$
= 52

The root are real and unequal.

Case 3: unequal and imaginary

The discriminant is less then 0 is known as unequal and imaginary.

Example:

= $$4^2 – 4x + 3$$
= $$a = 4, b = 4, c = 3$$
= $$b^2 – 4ac$$
= $$4^2 – 4(4)(3)$$
= $$16 – 48$$
= 52

The root are unequal and imaginary.

• Embed Calculator Widget
• Direct URL