1 The cubic equation \(2 x ^ { 3 } + x ^ { 2 } - p x - 5 = 0\), where \(p\) is a positive constant, has roots \(\alpha , \beta , \gamma\).
- State, in terms of \(p\), the value of \(\alpha \beta + \beta \gamma + \gamma \alpha\).
- Find the value of \(\alpha ^ { 2 } \beta \gamma + \alpha \beta ^ { 2 } \gamma + \alpha \beta \gamma ^ { 2 }\).
- Deduce a cubic equation whose roots are \(\alpha \beta , \beta \gamma , \alpha \gamma\).
- Given that \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = \frac { 1 } { 3 }\), find the value of \(p\).