| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2004 |
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| Session | November |
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| Topic | Roots of polynomials |
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3 Given that
$$\alpha + \beta + \gamma = 0 , \quad \alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = 14 , \quad \alpha ^ { 3 } + \beta ^ { 3 } + \gamma ^ { 3 } = - 18$$
find a cubic equation whose roots are \(\alpha , \beta , \gamma\).
Hence find possible values for \(\alpha , \beta , \gamma\).