What is DISCRIMINANT?: Nature of roots & how to find it?


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).