| Exam Board | OCR MEI |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2011 |
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| Session | June |
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| Topic | Roots of polynomials |
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3 The equation \(x ^ { 3 } + p x ^ { 2 } + q x + 3 = 0\) has roots \(\alpha , \beta\) and \(\gamma\), where
$$\begin{gathered}
\alpha + \beta + \gamma = 4
\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = 6
\end{gathered}$$
Find \(p\) and \(q\).