Answer
$-\frac{1}{2},\pm i$
Work Step by Step
1. List possible rational zeros $\pm1,\pm1/2,\pm1/4$
2. Use synthetic division, test these values and do not forget about the multiplicity (m) of each zero.
3 We can find a zero of $-1/2, m=2$ as shown.
4. $P=(2x+1)^2(x^2+1)$
5. Zeros $-\frac{1}{2},\pm i$
