8 The cubic equation \(x ^ { 3 } - x ^ { 2 } - 3 x - 10 = 0\) has roots \(\alpha , \beta , \gamma\).
- Let \(u = - \alpha + \beta + \gamma\). Show that \(u + 2 \alpha = 1\), and hence find a cubic equation having roots \(- \alpha + \beta + \gamma\), \(\alpha - \beta + \gamma , \alpha + \beta - \gamma\).
- State the value of \(\alpha \beta \gamma\) and hence find a cubic equation having roots \(\frac { 1 } { \beta \gamma } , \frac { 1 } { \gamma \alpha } , \frac { 1 } { \alpha \beta }\).