- The quadratic equation
$$4 x ^ { 2 } + 3 x + k = 0$$
where \(k\) is an integer, has roots \(\alpha\) and \(\beta\)
- Write down, in terms of \(k\) where appropriate, the value of \(\alpha + \beta\) and the value of \(\alpha \beta\)
- Determine, in simplest form in terms of \(k\), the value of \(\frac { \alpha } { \beta ^ { 2 } } + \frac { \beta } { \alpha ^ { 2 } }\)
- Determine a quadratic equation which has roots
$$\frac { \alpha } { \beta ^ { 2 } } \text { and } \frac { \beta } { \alpha ^ { 2 } }$$
giving your answer in the form \(p x ^ { 2 } + q x + r = 0\) where \(p , q\) and \(r\) are integer values in terms of \(k\)