2 In this question you must show detailed reasoning.
The equation \(z ^ { 4 } + 4 z ^ { 3 } + 9 z ^ { 2 } + 10 z + 6 = 0\) has roots \(\alpha , \beta , \gamma\) and \(\delta\).
- Show that a quartic equation whose roots are \(\alpha + 1 , \beta + 1 , \gamma + 1\) and \(\delta + 1\) is \(w ^ { 4 } + 3 w ^ { 2 } + 2 = 0\).
- Hence determine the exact roots of the equation \(z ^ { 4 } + 4 z ^ { 3 } + 9 z ^ { 2 } + 10 z + 6 = 0\).