Consider the function:
$f(z) = \dfrac{1}{z^{4}+z^{2}+1}$
I want to find the poles. I have deduced that there are 4 simple poles and 2 of them are in the upper half-plane. I'm not sure how I can find them, I have tried to find the zeros of $z^{4}+z^{2}+1$, but with no luck. I have also tried to see if I can factorize $z^{4}+z^{2}+1$, but I'm still stuck.