Answer
$-i, \pm5i$.
Work Step by Step
Step 1. Use the given coefficients of the polynomial to set up a division as shown in the figure.
Step 2. Perform synthetic divisions (note that $-i$ is also a zero) and find the quotient as $x^2+25$.
Step 3. Solve $x^2+25=0$ to get $x=\pm5i$.