Q. 83.7( 32 Votes )

If a is a zero of polynomial f(x) and (x – b) is the factor of polynomial g(x). Find value of a.g(b) – b. f(a)

Answer :

Concept Used:

Factor theorem: If (x – a) is a factor of f(x), then f(a) = 0


a is a zero of f(x), therefore, f(a) = 0

As (x – b) is a factor of g(x), g(b) = 0


a.g(b) – b.f(a) = a.0 – b.0 = 0

Hence, a.g(b) – b.f(a) = 0

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