Answer
$\{-\frac{1}{2},1,-2i,2i \}$
Work Step by Step
Step 1. Given $x=1,-2i$ as zeros, we can identify $x=2i$ is also a zero.
Step 2. Use synthetic divisions as shown in the figure to get a quotient as $2x+1$
Step 3. Solve $2x+1=0$ to get $x=-\frac{1}{2}$
Step 4. The zeros are $\{-\frac{1}{2},1,-2i,2i \}$
