The positive value of k for which x^{2} +Kx +64 = 0 & x^{2} - 8x + k = 0 will have real roots .
Ans: x^{2} + Kx + 64 = 0
⇒ b^{2} -4ac > 0
K^{2} - 256 > 0
K > 16 or K < - 16 ...............(1)
x^{2} - 8x + K = 0
64 - 4K > 0
⇒ 4K < 64
K < 16 ...............(2) From (1) & (2) K = 16