Estimate root of given equations, Mathematics

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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

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