Question

13. Determine the positive value of k for which the quadratic equation x² + kx + 64 = 0 andx? -
8x + k = 0 will both have real and equal roots.
​

Answer 1

Step-by-step explanation:

If the equaion x2 + kx + 64=0 has real roots, then D>=0

k2 -256> = 0→ k2 > = 256 → k2 > = (16)2 → k> =16.- (1)

if the equation x2 - 8x + k =0 has real roots.

then D> = 0 → 64- 4k > = 0 → 4k<= 64 → k < =16 - (2)

from (1) and (2) we get k=16