4.
The cubic equation \(3 x ^ { 3 } - 9 x ^ { 2 } + 6 x + 2 = 0\) has roots \(\alpha , \beta\) and \(\gamma\).
- Write down the values of \(\alpha + \beta + \gamma , \alpha \beta + \beta \gamma + \gamma \alpha\) and \(\alpha \beta \gamma\).
The cubic equation \(x ^ { 3 } + a x ^ { 2 } + b x + c = 0\) has roots \(\alpha ^ { 2 } , \beta ^ { 2 }\) and \(\gamma ^ { 2 }\).
- Show that \(c = - \frac { 4 } { 9 }\) and find the values of \(a\) and \(b\).
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