9 A cubic equation \(x ^ { 3 } + b x ^ { 2 } + c x + d = 0\) has real roots \(\alpha , \beta\) and \(\gamma\) such that
$$\begin{aligned}
\frac { 1 } { \alpha } + \frac { 1 } { \beta } + \frac { 1 } { \gamma } & = - \frac { 5 } { 12 }
\alpha \beta \gamma & = - 12
\alpha ^ { 3 } + \beta ^ { 3 } + \gamma ^ { 3 } & = 90
\end{aligned}$$
- Find the values of \(c\) and \(d\).
- Express \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 }\) in terms of \(b\).
- Show that \(b ^ { 3 } - 15 b + 126 = 0\).
- Given that \(3 + \mathrm { i } \sqrt { } ( 12 )\) is a root of \(y ^ { 3 } - 15 y + 126 = 0\), deduce the value of \(b\).