| Exam Board | OCR |
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| Module | Further Pure Core 1 (Further Pure Core 1) |
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| Year | 2024 |
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| Session | June |
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| Topic | Roots of polynomials |
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4 In this question you must show detailed reasoning.
The equation \(2 x ^ { 3 } + 3 x ^ { 2 } + 6 x - 3 = 0\) has roots \(\alpha , \beta\) and \(\gamma\).
Determine a cubic equation with integer coefficients that has roots \(\alpha ^ { 2 } \beta \gamma , \alpha \beta ^ { 2 } \gamma\) and \(\alpha \beta \gamma ^ { 2 }\).