Question

What will be the value of k, so that the roots of the equation are x^2 + 2kx + 9 are imaginary?

(a) -5 < k < 5

(b) -3 < k < 3

(c) 3 < k <  -3

(d) -5 < k < 3

This question was addressed to me in an interview for internship.

My question is taken from Quadratic Equation topic in chapter Quadratic Equation of Mathematics – Class 10

Answer 1

Correct choice is (b) -3 < k < 3

The best I can explain: Roots are imaginary. ∴ b^2 – 4ac < 0

(2k)^2 – 4(9)(1) < 0

4k^2 – 36 < 0

k^2 – 9 < 0

k^2 < 9

k < ±3

-3 < k < 3