Write down the values of a, b and c.

Step 2:

The discriminant formula is given by

Substitute the values in this formula and get the answer.

Below are given some solved examples based on the discriminant which may be helpful for you.

### Solved Examples

**Question 1: **Find the discriminant of the following equation:
x

^{2} - 2x + 1

** Solution: **

Given: x^{2} - 2x + 1 is a quadratic equation

Here a = 1, b = -2 and c = 1

The discriminant is given by

D = b^{2} - 4ac

= (-2)^{2} - 4(1)(1)

= 4 - 4
= 0.

The quadratic equation will be having only one real root.

**Question 2: **Find the discriminant of the following equation:
4x

^{2} - 5x + 1

** Solution: **

Given: 4x^{2} - 5x + 1 is a quadratic equation

Here a = 4, b = -5 and c = 1

The discriminant is given by

D = b^{2} - 4ac
= (-5)^{2} - 4(4)(1)

= 25 - 16
= 9.

This quadratic equation will be having two real solutions.

**Question 3: **Find the discriminant of the following equation:
3x

^{2} + x + 2

** Solution: **

Given: 3x^{2} + x + 2 is a quadratic equation

Here a = 1, b = -2 and c = 1

The discriminant is given by

D = b^{2} - 4ac

= (1)^{2} - 4(3)(2)

= 1 - 24
= -23.

The quadratic equation will be having two imaginary roots.