TITLE: Polynomial Equation Problem with Complex Roots
QUESTION [5 upvotes]: How could one find the complex or imaginary roots of any equations like
$$x+\sqrt[3]{x}-2=0$$
One of its roots is $1$, but what is/are the other/s?

REPLY [2 votes]: Let $\sqrt[3]{x}=t$.
Hence, we have: $$t^3+t-2=0$$ or:
$$t^3-t^2+t^2-t+2t-2=0$$ or:
$$(t-1)(t^2+t+2)=0,$$ which gives:
$$\sqrt[3]{x}=-\frac{1}{2}\pm\frac{\sqrt7}{2}i$$ or: $x=1$.