3 The quartic equation $\mathrm { x } ^ { 4 } + \mathrm { bx } ^ { 3 } + \mathrm { cx } ^ { 2 } + \mathrm { dx } - 2 = 0$ has roots $\alpha , \beta , \gamma , \delta$. It is given that

$$\alpha + \beta + \gamma + \delta = 3 , \quad \alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } + \delta ^ { 2 } = 5 , \quad \alpha ^ { - 1 } + \beta ^ { - 1 } + \gamma ^ { - 1 } + \delta ^ { - 1 } = 6$$

(a) Find the values of $b , c$ and $d$.\\

(b) Given also that $\alpha ^ { 3 } + \beta ^ { 3 } + \gamma ^ { 3 } + \delta ^ { 3 } = - 27$, find the value of $\alpha ^ { 4 } + \beta ^ { 4 } + \gamma ^ { 4 } + \delta ^ { 4 }$.\\

\hfill \mbox{\textit{CAIE Further Paper 1 2023 Q3}}