Question

$$6x^{3}+s4x=0$$

Solve for s_4 (complex solution)

$\left\{\begin{matrix}\\s_{4}=-6x^{2}\text{, }&\text{unconditionally}\\s_{4}\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$

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Solve for s_4

$\left\{\begin{matrix}\\s_{4}=-6x^{2}\text{, }&\text{unconditionally}\\s_{4}\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$

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Solve for x (complex solution)

$x=\frac{i\sqrt{6s_{4}}}{6}$
$x=0$
$x=-\frac{i\sqrt{6s_{4}}}{6}$

Solve for x

$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{\sqrt{-6s_{4}}}{6}\text{; }x=-\frac{\sqrt{-6s_{4}}}{6}\text{, }&s_{4}\leq 0\end{matrix}\right.$