| Exam Board | OCR MEI |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2013 |
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| Session | June |
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| Topic | Roots of polynomials |
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6 The cubic equation \(x ^ { 3 } - 5 x ^ { 2 } + 3 x - 6 = 0\) has roots \(\alpha , \beta\) and \(\gamma\). Find a cubic equation with roots \(\frac { \alpha } { 3 } + 1 , \frac { \beta } { 3 } + 1\) and \(\frac { \gamma } { 3 } + 1\), simplifying your answer as far as possible.