Question

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

Answer 1

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

pls brainliest