If (x - 6) is the HCF of x 2 - 2x - 24 and x 2- kx - 6, then what is the value of k?

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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

If (x - 6) is the HCF of x 2 - 2x - 24 and x 2- kx - 6, then what is the value of k?

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