| Exam Board | AQA |
|---|
| Module | Further AS Paper 1 (Further AS Paper 1) |
|---|
| Session | Specimen |
|---|
| Marks | 5 |
|---|
| Topic | Roots of polynomials |
|---|
11 The equation \(x ^ { 3 } - 8 x ^ { 2 } + c x + d = 0\) where \(c\) and \(d\) are real numbers, has roots \(\alpha , \beta , \gamma\).
When plotted on an Argand diagram, the triangle with vertices at \(\alpha , \beta , \gamma\) has an area of 8 .
Given \(\alpha = 2\), find the values of \(c\) and \(d\).
Fully justify your solution.
[0pt]
[5 marks]