**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 ax
^{2}+ bx + c = 0 is a quadratic equation, then the Discriminant of the equation, i.e. D = b2 – 4ac.

**More about Discriminant**

- 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 6x
^{2}+ 11x - 2 = 0 can be found by using discriminant D = b^{2}– 4ac.6x2 + 11x - 2 = 0

D = b^{2}– 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

- Find out the number of solutions the given equation has, by using its discriminant. Check whether the solutions are real or imaginary.

36x

A. 1 real and 1 imaginary solution

B. 2 real solutions

C. 2 imaginary solutions

D. None of the above

**Related Terms for Discriminant**

- Imaginary
- Quadratic equation
- Roots of a Quadratic Equation
- Solution