4 The quadratic equation \(x ^ { 2 } + x + k = 0\) has roots \(\alpha\) and \(\beta\).
- Use the substitution \(x = 2 u + 1\) to obtain a quadratic equation in \(u\).
- Hence, or otherwise, find the value of \(\left( \frac { \alpha - 1 } { 2 } \right) \left( \frac { \beta - 1 } { 2 } \right)\) in terms of \(k\).