# Discriminant calculator | Discriminant of a quadratic equation

## Discriminant calculator

x2 + x + =

With the Discriminant Calculator with steps that we put in your hands here, you will be able to calculate the discriminant of a quadratic equation, with which you will be able to have information about the nature of the roots of the equation.

To use the discriminant calculator perform these two simple steps:

1. Enter the value of each of the coefficients of the second degree equation.
2. Press the calculate button to obtain the calculation of the discriminant explained step by step.

## What's a discriminant in math?

The discriminant is a numerical value that is used to analyze the solutions of a quadratic equation.
Starting from a quadratic equation written in its standard form:

ax2 + bx + c = 0

The discriminant is calculated from the coefficients a, b and c of the quadratic equation, using the formula:

D = b2 − 4ac
Discriminant formula

If the discriminant is positive, D>0, then the quadratic equation has two real and distinct solutions.

If the discriminant is zero, D=0, then the quadratic equation has a double real solution.

If the discriminant is negative, D<0, then the quadratic equation has no real solutions, but it can have complex solutions (involving imaginary numbers).

## How to find the discriminant of a quadratic equation

Here are the steps to find the discriminant:
1. Identify the values of a, b, and c in the quadratic equation ax2 + bx + c = 0.
2. Substitute the values of a, b, and c into the formula D = b2 − 4ac.
3. Simplify the expression by performing the necessary operations, such as multiplication and addition.
4. The resulting value is the discriminant of the quadratic equation.

## Examples

### Example 01: Find the discriminant for this equation x2+3x+1 = 0

1x2 + 3x + 1 = 0

D = b2 − 4ac

a = 1
b = 3
c = 1

D = (3)2 − 4(1)(1)
D = 9 - 4

D = 5

The quadratic equation has two distinct real roots.

### Example 02: Find the discriminant of the quadratic equation x2+4x+7 = 0

1x2 + 4x + 7 = 0

D = b2 − 4ac

a = 1
b = 4
c = 7

D = (4)2 − 4(1)(7)
D = 16 - 28

D = -12

The quadratic equation has no real roots.