Obviously $z=0$ gives a zero. However now I'm stuck because it is not so easy to solve a fifth degree polynomial equation. Is there maybe a trick from complex analysis we can apply?
2026-03-30 15:36:16.1774884976
What are the zeros of $z^6-5z^4+z^3-2z \in \mathbb{C}$ within the unit circle?
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By Rouché's theorem, your polynomial has as many zeros within the unit circle (counting with multiplicity) as the polynomial $-5z^4$. That is, it has four zeros.