2. The quadratic equation
$$5 x ^ { 2 } - 4 x + 2 = 0$$
has roots \(\alpha\) and \(\beta\).
- Write down the value of \(\alpha + \beta\) and the value of \(\alpha \beta\).
- Find the value of \(\alpha ^ { 2 } + \beta ^ { 2 }\).
- Find a quadratic equation which has roots
$$\frac { 1 } { \alpha ^ { 2 } } \text { and } \frac { 1 } { \beta ^ { 2 } }$$
giving your answer in the form \(p x ^ { 2 } + q x + r = 0\), where \(p , q\) and \(r\) are integers.
\includegraphics[max width=\textwidth, alt={}, center]{4da2bb2c-a51b-493c-a9f2-f4ff008a3aac-07_70_51_2663_1896}