Question

$$A x _{ 2 } +Bx+C=0$$

Solve for A (complex solution)

$\left\{\begin{matrix}A=-\frac{Bx+C}{x_{2}}\text{, }&x_{2}\neq 0\\A\in \mathrm{C}\text{, }&C=-Bx\text{ and }x_{2}=0\end{matrix}\right.$

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Solve for B (complex solution)

$\left\{\begin{matrix}B=-\frac{Ax_{2}+C}{x}\text{, }&x\neq 0\\B\in \mathrm{C}\text{, }&C=-Ax_{2}\text{ and }x=0\end{matrix}\right.$

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Solve for A

$\left\{\begin{matrix}A=-\frac{Bx+C}{x_{2}}\text{, }&x_{2}\neq 0\\A\in \mathrm{R}\text{, }&C=-Bx\text{ and }x_{2}=0\end{matrix}\right.$

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Solve for B

$\left\{\begin{matrix}B=-\frac{Ax_{2}+C}{x}\text{, }&x\neq 0\\B\in \mathrm{R}\text{, }&C=-Ax_{2}\text{ and }x=0\end{matrix}\right.$

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