Question

The value of k(k > 0) for which the equation x² + kx + 64 = 0 and x² – 8x + k = 0 both will have real roots is –

• A. 8
• B. –16
• C. – 64
• D. 16

Answer 1

Answer: (D)

16

Answer 2

x² + kx + 64 = 0

⇒ k²– 4 × 64 ≥ 0 ⇒ k ≥ 16

x² – 8x + k = 0 ⇒ 64 – 4k ≥ 0 ⇒ k $\leq$ 16

∴ k = 16