Discriminant
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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 = b^{2}  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.
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 solutionB. 2 real solutions
C. 2 imaginary solutions
D. None of the above
Correct Answer: D
Solution:

Step 1: 36x^{2} + 132x + 121 = 0
Step 2: Compare the equation with the standard form ax^{2} + bx + c = 0 to get the values of a, b and c.
Step 3: b^{2}  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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