Q24 of 32 Page 2

If (x2 – 1) is a factor of ax4 + bx3 + cx2 + dx + e. Then, prove that

a – b + c = d – e

Concept Used:


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


Explanation:


Let f(x) = ax4 + bx3 + cx2 + dx + e


If (x2 – 1) is a factor of f(x), then (x + 1) and (x – 1) are the factors of f(x).


Therefore, f(1) = f(–1) = 0


f(1) = a + b + c + d + e = 0


f(–1) = a – b + c – d + e = 0


a + c + e = b + d


a – b + c = d – e


Hence, Proved.


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