9 A cubic equation \(x^{3}+b x^{2}+c x+d=0\) has real roots \(\alpha, \beta\) and \(\gamma\) such that
\(\begin{aligned}
\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma} & =-\frac{5}{12}, \\
\alpha \beta \gamma & =-12, \\
\alpha^{3}+\beta^{3}+\gamma^{3} & =90 .
\end{aligned}\)
(i) Find the values of \(c\) and \(d\).

(ii) Express \(\alpha^{2}+\beta^{2}+\gamma^{2}\) in terms of \(b\).

(iii) Show that \(b^{3}-15 b+126=0\).

(iv) Given that \(3+\mathrm{i} \sqrt{ }(12)\) is a root of \(y^{3}-15 y+126=0\), deduce the value of \(b\).