Question

For what values of k the roots of the quadratic equation 9x² + 3kx + 4 = 0 are real and equal?

(A) ±4

(B) ±7

(C) ±9

(D) ±6

Answer 1

Correct option is (A) ±4

A quadratic equation ax² + bx + c = 0 has discriminant D = b² − 4ac

As per concept of nature of roots, for repeated roots, D = b² − 4ac = 0

Here, a = 9, b = 3k, c = 4

∴ (3k)² − 4 × 9 × 4 = 0

⇒ 9k² = 4 × 9 × 4 

⇒ k = ±4