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If the polynomial f(x) = ax3 + bx – c is divisible by the polynomial g(x) = x2 + bx + c, then ab =
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