The function $\mathrm{f}$ is defined by $\mathrm{f}(z)=a z^{3}+b z^{2}+c z+d$, where $a, b, c$ and $d$ are real numbers. Given that $2+\mathrm{i}$ and $-3$ are roots of $\mathrm{f}(z)=0$, find $b, c$ and $d$ in terms of $a$.

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