3 The cubic equation \(z ^ { 3 } + 4 z ^ { 2 } - 3 z + 1 = 0\) has roots \(\alpha , \beta\) and \(\gamma\).
- Write down the values of \(\alpha + \beta + \gamma , \alpha \beta + \beta \gamma + \gamma \alpha\) and \(\alpha \beta \gamma\).
- Show that \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = 22\).