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

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

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Eliza 1 month 2021-08-13T11:50:55+00:00 1 Answer 0 views 0

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    2021-08-13T11:52:16+00:00

    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 – 2×1 – 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

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