| Exam Board | OCR MEI |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2012 |
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| Session | January |
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| Topic | Roots of polynomials |
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5 The equation \(z ^ { 3 } - 5 z ^ { 2 } + 3 z - 4 = 0\) has roots \(\alpha , \beta\) and \(\gamma\). Find the cubic equation whose roots are \(\frac { \alpha } { 2 } + 1 , \frac { \beta } { 2 } + 1\), \(\frac { \gamma } { 2 } + 1\), expressing your answer in a form with integer coefficients.