Question

If (x – 6) is the H.C.F of x2

– 2x – 24 and x2

– kx – 6 then the value of k is __​

Answer 1

Answer:

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Step-by-step explanation:

Correct Option: B

Given that, (x - 6) is the HCF of x2 - 2x - 24 and x2 - kx - 6 i.e., (x - 6) is a factor of both expressions.

Let f (x1) = x12 - 2x1 - 24

and f (x2) = x22 - kx2 - 6

Now f(x1) = f (x2) at (x1 = x2 = 6)

⇒ (6)2 - 2(6) - 24 = (6)2 - k(6) - 6 [by condition]

⇒ 0 = 30 - 6k ⇒ 6 k = 30

∴ k = 5