Q14 of 109 Page 3

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

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