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  • If x plus1 is a factor of ax qube plus x square minus 2x plus 4a minus 9 , find the value of a.

If x+1  is a factor of ax^{3}+x^{2}-2x+4a-9 , find the value of a.

Answers (1)

a = 2

Solution:

We know that if (x+a)  is factor of the polynomial f(x), then it always satisfies f(-a)=0

Given x+1  is a factor of ax^{3}+x^{2}-2x+4a-9

Let       p(x)=ax^{3}+x^{2}-2x+4a-9

g(x)=x+1

According to remainder theorem if g(x) is a factor of p(x) then p(-1)=0

\\p(-1)=a(-1)^{3}+(-1)^{2}-2(-1)+4a-9\\ 0=-a+1+2+4a-9\\ 0=3a-6\\ 3a=6\\ a=\frac{6}{3}=2

Hence a = 2.

 

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infoexpert24

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