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.
Question: Find out the number of solutions the given equation has, by using its discriminant. Check whether the solutions are real or imaginary.
36×2 + 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.