3 The quartic equation \(x ^ { 4 } + 2 x ^ { 3 } - 1 = 0\) has roots \(\alpha , \beta , \gamma , \delta\).
- Find a quartic equation whose roots are \(\alpha ^ { 4 } , \beta ^ { 4 } , \gamma ^ { 4 } , \delta ^ { 4 }\) and state the value of \(\alpha ^ { 4 } + \beta ^ { 4 } + \gamma ^ { 4 } + \delta ^ { 4 }\).
- Find the value of \(\alpha ^ { 5 } + \beta ^ { 5 } + \gamma ^ { 5 } + \delta ^ { 5 }\).
- Find the value of \(\alpha ^ { 8 } + \beta ^ { 8 } + \gamma ^ { 8 } + \delta ^ { 8 }\).