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FM June 2024 p13 q02
4172
The cubic equation \(x^3 + 2x^2 + 3x + 1 = 0\) has roots \(\alpha, \beta, \gamma\).
(a) Find a cubic equation whose roots are \(\alpha^2 + 1, \beta^2 + 1, \gamma^2 + 1\).
(b) Find the value of \((\alpha^2 + 1)^2 + (\beta^2 + 1)^2 + (\gamma^2 + 1)^2\).
(c) Find the value of \((\alpha^2 + 1)^3 + (\beta^2 + 1)^3 + (\gamma^2 + 1)^3\).
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