Q. 14.4( 275 Votes )

If (x + 1) is a factor of f(x) = ax2 – x + 1. Find the value of a.

Answer :

Concept Used:


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


Explanation:


If (x + 1) is a factor of f(x), then f(–1) = 0


f(x) = ax2 – x + 1


f(–1) = a(-1)2 – (-1) + 1


f(–1) = a + 1 + 1
        = a + 2

As f(–1) = 0

So,

a + 2 = 0
a = -2 

Hence, a = -2.

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