Question 30
Show that in the case that the equations
$$
\begin{aligned}
& x^{3}+m x-n=0 \\
& n x^{3}-2 m^{2} x^{2}-5 m n x-2 m^{3}-n^{2}=0
\end{aligned}
$$
$(n \neq 0)$, have a common root, the first will have two equal roots, and then determine the roots of the two equations based on $n$.
$$
\begin{aligned}
& x^{3}+m x-n=0 \\
& n x^{3}-2 m^{2} x^{2}-5 m n x-2 m^{3}-n^{2}=0
\end{aligned}
$$
$(n \neq 0)$, have a common root, the first will have two equal roots, and then determine the roots of the two equations based on $n$.