5.
The equation \(z ^ { 3 } + k z ^ { 2 } + 9 = 0\) has roots \(\alpha , \beta\) and \(\gamma\).
- Show that
$$\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = k ^ { 2 }$$
- (ii) Show that
$$\alpha ^ { 2 } \beta ^ { 2 } + \beta ^ { 2 } \gamma ^ { 2 } + \gamma ^ { 2 } \alpha ^ { 2 } = - 18 k$$