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.

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 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.

Video Examples: Free Math Lessons The Discriminant
 

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
Correct Answer: D

Solution:

Step 1: 36x² + 132x + 121 = 0 
Step 2: Compare the equation with the standard form ax² + bx + c = 0 to get the values of a, b and c.
Step 3: b² - 4ac = (132)² - 4(36)(121) [Substitute the values.] 
Step 4: = 17424 - 17424 = 0 [Simplify.]
Step 5: Since the discriminant is zero, the quadratic equation has one real solution.

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