5. The quadratic equation
$$4 x ^ { 2 } + 3 x + 1 = 0$$
has roots \(\alpha\) and \(\beta\).
- Write down the value of \(( \alpha + \beta )\) and the value of \(\alpha \beta\).
- Find the value of \(\left( \alpha ^ { 2 } + \beta ^ { 2 } \right)\).
- Find a quadratic equation which has roots
$$( 4 \alpha - \beta ) \text { and } ( 4 \beta - \alpha )$$
giving your answer in the form \(p x ^ { 2 } + q x + r = 0\) where \(p , q\) and \(r\) are integers to be determined.