| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2008 |
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| Session | June |
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| Topic | Roots of polynomials |
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5 The equation
$$x ^ { 3 } + x - 1 = 0$$
has roots \(\alpha , \beta , \gamma\). Show that the equation with roots \(\alpha ^ { 3 } , \beta ^ { 3 } , \gamma ^ { 3 }\) is
$$y ^ { 3 } - 3 y ^ { 2 } + 4 y - 1 = 0$$
Hence find the value of \(\alpha ^ { 6 } + \beta ^ { 6 } + \gamma ^ { 6 }\).