- The roots of the equation
$$2 x ^ { 3 } - 3 x ^ { 2 } + 12 x + 7 = 0$$
are \(\alpha , \beta\) and \(\gamma\)
Without solving the equation,
- write down the value of each of
$$\alpha + \beta + \gamma \quad \alpha \beta + \alpha \gamma + \beta \gamma \quad \alpha \beta \gamma$$
- Use the answers to part (a) to determine the value of
- \(\frac { 2 } { \alpha } + \frac { 2 } { \beta } + \frac { 2 } { \gamma }\)
- \(( \alpha - 1 ) ( \beta - 1 ) ( \gamma - 1 )\)
- \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 }\)