If the HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x – k), the – InterviewSolution

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1.

If the HCF of (x2 + x – 12) and (2x2 – kx – 9) is (x – k), then what is the value of k ?

Answer»

Since (x – k) is the HCF of (x² + x + 12) and (2x² – kx – 9)

(x – k) will be a factor of 2x² – kx – 9

∴ 2.k² – k.k – 9 = 0 ⇒ k² – 9 = 0 ⇒ k = ± 3

Also, the factors of (x² + x – 12) = (x + 4) (x – 3) ∴ k = 3.

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