The values of k for which the quadratic equation 16x^2 + 4kx + 9 = 0 has real and equal roots. A. 6, (-1)/6 B. 36, -36 C. 6, - 6

Question

The values of k for which the quadratic equation 16x² + 4kx + 9 = 0 has real and equal roots.

A. \(6,-\frac{1}{6}\)

B. 36, – 36

C. 6, – 6

D. \(\frac{3}{4},-\frac{3}{4}\)

Answer 1

Given: 16x² + 4kx + 9 = 0

To find: The values of k for which the quadratic equation 16x² + 4kx + 9 

= 0 has real and equal roots.

Solution: To have real and equal roots d 

= 0Where d = b² – 4ac

⇒b² – 4ac = 0Compare with the general equation of quadratic equation 

ax² + bx + c = 0, a ≠ 0

here a = 16, b = 4k and c = 9

⇒b² – 4ac =(4k)² – 4 x 16 x 9 = 0

⇒16 k² – 576 = 0 

⇒k² = 576 /16 

⇒k = 24/ 4

k = \(\pm6\)