| Exam Board | OCR MEI |
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| Module | Further Pure Core AS (Further Pure Core AS) |
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| Year | 2022 |
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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 \(z ^ { 3 } + 2 z ^ { 2 } + k z + 3 = 0\), where \(k\) is a constant, has roots \(\alpha , \frac { 1 } { \alpha }\) and \(\beta\).
Determine the roots in exact form.