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

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