If the polynomial f(x) = ax 3 + bx – c is divisible by the polynomial g(x) = x 2 + bx + c, then ab =

Question

Philoid · Accepted Answer

Given;

f(x) = ax³ + bx – c is divisible by g(x) = x² + bx + c

Now by division Method,

As f(x) is divisible by g(x), then remainder must be 0,

i.e.

(ab² – ac + b)x + c(ab – 1) = 0

⇒ (ab² – ac + b)x = 0 and c(ab – 1) = 0

⇒ ab² – ab + b = 0 (∵ x ≠ 0) and ab – 1 = 0 (∵ c ≠ 0)

⇒ ab – 1 = 0

⇒ ab = 1