7 The function \(\mathrm { f } ( z ) = 2 z ^ { 4 } - 9 z ^ { 3 } + A z ^ { 2 } + B z - 26\) has real coefficients. The equation \(\mathrm { f } ( z ) = 0\) has two real roots, \(\alpha\) and \(\beta\), where \(\alpha > \beta\), and two complex roots, \(\gamma\) and \(\delta\), where \(\gamma = 3 + 2 \mathrm { j }\).

1. Show that \(\alpha + \beta = - \frac { 3 } { 2 }\) and find the value of \(\alpha \beta\).
2. Hence find the two real roots \(\alpha\) and \(\beta\).
3. Find the values of \(A\) and \(B\).
4. Write down the roots of the equation \(\mathrm { f } \left( \frac { w } { \mathrm { j } } \right) = 0\).