# What is Discriminant?

The discriminant is the way of finding the nature of roots(

*values of variable)*. Roots are distinct, equal or will not real, we will find with the help of discriminant.It is applicable for quadratic equation whose general form is-

*ax² + bx + c = 0*The formula of discriminant will be-

D = b² - 4ac

Where,

D = Discriminant

b = coefficient of x

a = coefficient of x²

c = constant term

## How discriminant show the nature of roots?

We find the nature of roots with the help of below conditions-

1.) Discriminant D give distinct

*(different)*roots if-

**b² - 4ac > 0**

*(Greater than zero)*

2.) Discriminant D give equal

*(same)*roots if-

**b² - 4ac = 0**

*(Equal to zero)*

3.) Discriminant D give no real roots if-

**b² - 4ac < 0**

*(Less than zero)*

## How to find the nature of roots?

For finding the nature of roots we need to understand some examples-

*1. Example:-*

Find the discriminant of the quadratic equation 2x² - 4x + 3 = 0 & also find the nature of roots.

Solve:-

First, we will compare given quadratic equation from general form-

2x² - 4x + 3=0

ax² + bx + c = 0

Where, a=2, b=-4 & c=3

Now, we will find the discriminant of the given quadratic equation-

= b² - 4ac

Putting all the values-

= (-4)² - (4×2×3)

= 16 - 24

= -8

= -8 < 0

Here discriminant b²-4ac < 0 ( Less than zero)

**So we get no real roots**(Nature of roots).

*2. Example:-*

Find the discriminant of the quadratic equation x² + 6x + 5 = 0 & also find the nature of roots.

Solve:-

First, we will compare given quadratic equation from general form-

x² + 6x + 5 =0

ax² + bx + c = 0

Where, a=1, b=6 & c=5

Now, we will find the discriminant of the given quadratic equation-

= b² - 4ac

Putting all the values-

= (6)² - (4×1×5)

= 36 - 20

= 16

= 16 > 0

Here discriminant b²-4ac > 0 ( Greater than zero)

**So we get distinct real roots**(Nature of roots).