- The quadratic equation
$$2 x ^ { 2 } + 4 x - 3 = 0$$
has roots \(\alpha\) and \(\beta\).
Without solving the quadratic equation,
- find the exact value of
- \(\alpha ^ { 2 } + \beta ^ { 2 }\)
- \(\alpha ^ { 3 } + \beta ^ { 3 }\)
- Find a quadratic equation which has roots ( \(\alpha ^ { 2 } + \beta\) ) and ( \(\beta ^ { 2 } + \alpha\) ), giving your answer in the form \(a x ^ { 2 } + b x + c = 0\), where \(a , b\) and \(c\) are integers.
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