1 The cubic equation \(x ^ { 3 } + b x ^ { 2 } + d = 0\) has roots \(\alpha , \beta , \gamma\), where \(\alpha = \beta\) and \(d \neq 0\).
- Show that \(4 b ^ { 3 } + 27 d = 0\).
- Given that \(2 \alpha ^ { 2 } + \gamma ^ { 2 } = 3 b\), find the values of \(b\) and \(d\).