Question

If $x=\frac{3+5i}{2}$, find the value of $2x^3+2x^2-7x+72$.

Answer 1

$x=\frac{3+5i}{2}$
$\Rightarrow 2x-3=5i$
on squaring, we get $\Rightarrow 4x^2+9-12x=-25$
$\Rightarrow x^2-6x+17=0$ ...(1)
Dividing $2x^3+2x^2-7x+72$ with $x^2-6x+17$, we get
$2x^3+2x^2-7x+72=(x^2-6x+17)(x+4)$
Therefore using (1), we get $2x^3+2x^2-7x+72=0$
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