Question

Find the nonzero value of k for which the roots of the quadratic equation 9x² – 3kx + k = 0 are real and equal.

Answer 1

The given equation is 9x² – 3kx + k = 0

This is of the form ax² + bx + c = 0, where a = 9, b = –3k and c = k 

∴ D = b² – 4ac

= (–3k)² – 4 × 9 × k

= 9k² – 36k 

The given equation will have real and equal roots if D = 0. 

∴ 9k² – 36k = 0  

⇒ 9k(k – 4) = 0 

⇒ k = 0 or k – 4 = 0 

⇒ k = 0 or k = 4 

But, k ≠ 0 (Given)

Hence, the required values of k is 4.