# Discriminant

## Definition Of Discriminant

The Discriminant of an equation gives an idea of the number of roots and the nature of roots of the equation.
If ax2 + bx + c = 0 is a quadratic equation, then the Discriminant of the equation, i.e. D = b2 - 4ac.

If discriminant (D) is equal to 0 then the equation has one real solution.
If D > 0, then the equation has two real solutions.
If D < 0,="" then="" the="" equation="" has="" two="" imaginary="" solutions.="">

### Example of Discriminant

The nature of roots of equation 6x2 + 11x - 2 = 0 can be found by using discriminant D = b2 - 4ac.6x2 + 11x - 2 = 0
D = b2 - 4ac = (11)2 - 4(6)(2) [Substitute the values.]
D = 121 - 48 = 73 > 0
As D > 0, the given equation has 2 real solutions.

### Solved Example on Discriminant

#### Ques: Find out the number of solutions the given equation has, by using its discriminant. Check whether the solutions are real or imaginary.  36x2 + 132x + 121 = 0

##### Choices:

A. 1 real and 1 imaginary solution
B. 2 real solutions
C. 2 imaginary solutions
D. None of the above