| Exam Board | CAIE |
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| 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 Find a cubic equation with roots \(\alpha , \beta\) and \(\gamma\), given that
$$\alpha + \beta + \gamma = - 6 , \quad \alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = 38 , \quad \alpha \beta \gamma = 30 .$$
Hence find the numerical values of the roots.