9231 P12 - Nov 2025 - Q2 - 8 marks
5889
(a) The cubic \(x^3+bx^2+cx+d=0\) has roots \(\alpha,\beta,\gamma\). Given \(\alpha+\beta+\gamma=2\), \(\alpha^2+\beta^2+\gamma^2=3\), and \(\alpha^4+\beta^4+\gamma^4=5\), find \(b\) and \(c\).
(b) Find the value of \(d\).
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