Let \( \alpha+i \beta ; \alpha, \beta \in \mathrm{R} \), be a root ...

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Let \( \alpha+i \beta ; \alpha, \beta \in \mathrm{R} \), be a root of the equation \( \mathrm{x}^{3}+\mathrm{qx}+\mathrm{r}=0 ; \mathrm{q}, \mathrm{r} \in \mathrm{R} \). Find a real cubic equation,
\( \mathrm{P} \) independent of \( \alpha \& \beta \), whose one root is \( 2 \alpha \).

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