2 Find the cubic equation with roots \(\alpha , \beta\) and \(\gamma\) such that
$$\begin{aligned}
\alpha + \beta + \gamma & = 3 \\
\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } & = 1 \\
\alpha ^ { 3 } + \beta ^ { 3 } + \gamma ^ { 3 } & = - 30
\end{aligned}$$
giving your answer in the form \(x ^ { 3 } + p x ^ { 2 } + q x + r = 0\), where \(p , q\) and \(r\) are integers to be found.
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2 Find the cubic equation with roots $\alpha , \beta$ and $\gamma$ such that
$$\begin{aligned}
\alpha + \beta + \gamma & = 3 \\
\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } & = 1 \\
\alpha ^ { 3 } + \beta ^ { 3 } + \gamma ^ { 3 } & = - 30
\end{aligned}$$
giving your answer in the form $x ^ { 3 } + p x ^ { 2 } + q x + r = 0$, where $p , q$ and $r$ are integers to be found.
\hfill \mbox{\textit{CAIE FP1 2016 Q2}}