- The cubic equation
$$2 x ^ { 3 } - 3 x ^ { 2 } + 5 x + 7 = 0$$
has roots \(\alpha , \beta\) and \(\gamma\).
Without solving the equation, determine the exact value of
- \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 }\)
- \(\frac { 3 } { \alpha } + \frac { 3 } { \beta } + \frac { 3 } { \gamma }\)
- \(( 5 - \alpha ) ( 5 - \beta ) ( 5 - \gamma )\)