| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2017 |
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| Session | June |
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| Topic | Roots of polynomials |
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7 By finding a cubic equation whose roots are \(\alpha , \beta\) and \(\gamma\), solve the set of simultaneous equations
$$\begin{aligned}
\alpha + \beta + \gamma & = - 1 ,
\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } & = 29 ,
\frac { 1 } { \alpha } + \frac { 1 } { \beta } + \frac { 1 } { \gamma } & = - 1 .
\end{aligned}$$