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

Given;

f(x) = ax^{3} + bx – c is divisible by g(x) = x^{2} + bx + c

Now by division Method,

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

i.e.

(ab^{2} – ac + b)x + c(ab – 1) = 0

⇒ (ab^{2} – ac + b)x = 0 and c(ab – 1) = 0

⇒ ab^{2} – ab + b = 0 (∵ x ≠ 0) and ab – 1 = 0 (∵ c ≠ 0)

⇒ ab – 1 = 0

⇒ ab = 1

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