Question

Find the value of k if (x-3) is a factor of k2x2-kx-2

Answer 1

Answer :

Let, f (x) = k²x² - kx - 2

Since (x - 3) is a factor of f (x),

f (3) = 0

⇒ k² (3²) - k (3) - 2 = 0

⇒ 9k² - 3k - 2 = 0

⇒ 9k² - 6k + 3k - 2 = 0

⇒ 3k (3k - 2) + 1 (3k - 2) = 0

⇒ (3k - 2) (3k + 1) = 0

∴ k = 2/3, - 1/3

Hope it helps! (: