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  • If x+2a is a factor of x^{5}-4a^{2}x^{3}+2x+2a+3 , find a.

If x+2a  is a factor of x^{5}-4a^{2}x^{3}+2x+2a+3 , find a.

Answers (1)

a=\frac{3}{2}

Solution

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

Given  x+2a is a factor of x^{5}-4a^{2}x^{3}+2x+2a+3

Let

p(x)=x^{5}-4a^{2}x^{3}+2x+2a+3

g(x)=x+2a

If g(x) is a factor of p(x), then p(-2a)=0
\\p(-2a)=(-2a)^{5}-4a^{2}(-2a)^{3}+2(-2a)+2a+3\\ 0=-32a^{5}+32a^{5}-4a+2a+3\\ 0=-2a+3\\ 2a=3\\

So, a=\frac{3}{2}

Posted by

infoexpert24

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