Question

The positive value of k for which the equation x² + kx + 64 = 0 and x² − 8x + k = 0 will both have real roots, is

(a) 4
(b) 8
(c) 12
(d) 16

Answer 1

The given quadric equation are , and roots are real.

Then find the value of a.

Here, ….. (1)

….. (2)

As we know that

Putting the value of

The given equation will have real and distinct roots, if

Therefore, putting the value of in equation (2) we get

The value of satisfying to both equations

Thus, the correct answer is