The roots of the quartic equation $x ^ { 4 } + 4 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 1 = 0$ are $\alpha , \beta , \gamma$ and $\delta$. Find the values of\\
(i) $\alpha + \beta + \gamma + \delta$,\\
(ii) $\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } + \delta ^ { 2 }$,\\
(iii) $\frac { 1 } { \alpha } + \frac { 1 } { \beta } + \frac { 1 } { \gamma } + \frac { 1 } { \delta }$,\\
(iv) $\frac { \alpha } { \beta \gamma \delta } + \frac { \beta } { \alpha \gamma \delta } + \frac { \gamma } { \alpha \beta \delta } + \frac { \delta } { \alpha \beta \gamma }$.

Using the substitution $y = x + 1$, find a quartic equation in $y$. Solve this quartic equation and hence find the roots of the equation $x ^ { 4 } + 4 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 1 = 0$.

\hfill \mbox{\textit{CAIE FP1 2014 Q11 EITHER}}