Answer
zeros: $\displaystyle \pm\frac{3}{2}i$, each multiplicity 1.
$P(x)=(2x-3i)(2x+3i)$
Work Step by Step
$4x^{2}+9=0$
$4x^{2}=-9$
$x^{2}=-\displaystyle \frac{9}{4}$
$x=\displaystyle \pm\frac{3}{2}i\qquad $ (zeros, each multiplicity of 1)
$(\displaystyle \pm\sqrt{-\frac{9}{4}}=\pm\sqrt{\frac{9}{4}}\cdot\sqrt{-1}=\pm\frac{3}{2}i)$
Factorization:
$4(x-\displaystyle \frac{3}{2}i)(x+\frac{3}{2}i)=2\cdot(x-\frac{3}{2}i)\cdot 2\cdot(x+\frac{3}{2}i)$
$=(2x-3i)(2x+3i)$
