3 The equation \(x ^ { 4 } - 2 x ^ { 3 } - 1 = 0\) has roots \(\alpha , \beta , \gamma , \delta\).
- Find a quartic equation whose roots are \(\alpha ^ { 3 } , \beta ^ { 3 } , \gamma ^ { 3 } , \delta ^ { 3 }\) and state the value of \(\alpha ^ { 3 } + \beta ^ { 3 } + \gamma ^ { 3 } + \delta ^ { 3 }\). [4]
- Find the value of \(\frac { 1 } { \alpha ^ { 3 } } + \frac { 1 } { \beta ^ { 3 } } + \frac { 1 } { \gamma ^ { 3 } } + \frac { 1 } { \delta ^ { 3 } }\).
- Find the value of \(\alpha ^ { 4 } + \beta ^ { 4 } + \gamma ^ { 4 } + \delta ^ { 4 }\).