| Exam Board | OCR MEI |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2014 |
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| Session | June |
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| Topic | Roots of polynomials |
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5 The roots of the cubic equation \(3 x ^ { 3 } - 9 x ^ { 2 } + x - 1 = 0\) are \(\alpha , \beta\) and \(\gamma\). Find the cubic equation whose roots are \(3 \alpha - 1,3 \beta - 1\) and \(3 \gamma - 1\), expressing your answer in a form with integer coefficients.