| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2016 |
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| Session | November |
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| Topic | Roots of polynomials |
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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.