8 In this question you must show detailed reasoning.
- Explain why all cubic equations with real coefficients have at least one real root.
- Points representing the three roots of the equation \(z ^ { 3 } + 9 z ^ { 2 } + 27 z + 35 = 0\) are plotted on an Argand diagram.
Find the exact area of the triangle which has these three points as its vertices.