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.

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.