the positive value of k for which x2 kx 64 0 amp

Question

The positive value of k for which x² +Kx +64 = 0 & x² - 8x + k = 0 will have real roots .

Ans: x² + Kx + 64 = 0

⇒ b² -4ac > 0

K² - 256 > 0

K > 16 or K < - 16                        ...............(1)

x² - 8x + K = 0

64 - 4K > 0

⇒ 4K < 64

K < 16                                       ...............(2) From (1) & (2)  K = 16