Q. 143.8( 12 Votes )

# If the polynomial f(x) = ax3 + bx – c is divisible by the polynomial g(x) = x2 + bx + c, then ab =A. 1B. C. –1D.

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

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