9231 P11 - Jun 2020 - Q2 - 8 marks
5809
2 The cubic equation \(6 x^{3}+p x^{2}-3 x-5=0\), where \(p\) is a constant, has roots \(\alpha, \beta, \gamma\).
(a) Find a cubic equation whose roots are \(\alpha^{2}, \beta^{2}, \gamma^{2}\).
(b) It is given that \(\alpha^{2}+\beta^{2}+\gamma^{2}=2(\alpha+\beta+\gamma)\).
(i) Find the value of \(p\).
(ii) Find the value of \(\alpha^{3}+\beta^{3}+\gamma^{3}\).
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