If x+2 a is a factor of x^{5}-4 a^{2} x^{3}+2 | vedclass

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Question

Let $p(x)=x^{5}-4 a^{2} x^{3}+2 x+2 a+3$

If $x-(-2 a)$ is a factor of $p ( x )$, then $p(-2 a)=0$

$	herefore$ $p(-2 a)=(-2 a)^{5}-4 a^{2}(-2 a)

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

Let $p(x)=x^{5}-4 a^{2} x^{3}+2 x+2 a+3$

If $x-(-2 a)$ is a factor of $p ( x )$, then $p(-2 a)=0$

$	herefore$ $p(-2 a)=(-2 a)^{5}-4 a^{2}(-2 a)^{3}+2(-2 a)+2 a+3$

$=-32 a^{5}+32 a^{5}-4 a+2 a+3$

$=-2 a+3$

Now, $\quad p(-2 a)=0$

$\Rightarrow \quad-2 a+3=0$

$\Rightarrow \quad a=\frac{3}{2}$

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

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