Question

Find the value of k for which the roots of 9x² + 8kx + 16 = 0 are real and equal.

Answer 1

Given: 

9x² + 8kx + 16 = 0

Here,  

a = 9, b = 8k and c = 16 

It is given that the roots of the equation are real and equal; therefore, we have: 

D = 0 

⇒ (b² – 4ac) = 0 

⇒ (8k)² – 4 × 9 × 16 = 0 

⇒ 64k² – 576 = 0 

⇒ 64k² = 576 

⇒ k² = 9  

⇒ k = ±3 

∴ k = 3 or k = –3