| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2011 |
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| Session | June |
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| Topic | Roots of polynomials |
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2 The roots of the equation
$$x ^ { 3 } + p x ^ { 2 } + q x + r = 0$$
are \(\frac { \beta } { k } , \beta , k \beta\), where \(p , q , r , k\) and \(\beta\) are non-zero real constants. Show that \(\beta = - \frac { q } { p }\).
Deduce that \(r p ^ { 3 } = q ^ { 3 }\).