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

Step-by-step explanation:

a-4 is the answer of your question

Answer 2

D. 16

Step-by-step explanation:

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

discriminant for equation one = k² - 4(64)

discriminant for equation two = 64 - 4k

If both have real roots, then d is a positive number for both cases.

So k² - 256 >= 0 ; k² >= 16² ---------------------(1)

 64 - 4k >= 0; 16 >= k ----------------(2)

From (1) and (2), we conclude that k = 16

Option D is the answer.