| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2007 |
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| Session | November |
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| Topic | Roots of polynomials |
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4 The roots of the equation
$$x ^ { 3 } - 8 x ^ { 2 } + 5 = 0$$
are \(\alpha , \beta , \gamma\). Show that
$$\alpha ^ { 2 } = \frac { 5 } { \beta + \gamma } .$$
It is given that the roots are all real. Without reference to a graph, show that one of the roots is negative and the other two roots are positive.