| Exam Board | AQA |
|---|
| Module | Further Paper 2 (Further Paper 2) |
|---|
| Year | 2024 |
|---|
| Session | June |
|---|
| Topic | Invariant lines and eigenvalues and vectors |
|---|
10 The matrix \(\mathbf { C }\) is defined by
$$\mathbf { C } = \left[ \begin{array} { c c }
3 & 2
- 4 & 5
\end{array} \right]$$
Prove that the transformation represented by \(\mathbf { C }\) has no invariant lines of the form \(y = k x\)
Latifa and Sam are studying polynomial equations of degree greater than 2 , with real coefficients and no repeated roots.
Latifa says that if such an equation has exactly one real root, it must be of degree 3
Sam says that this is not correct.
State, giving reasons, whether Latifa or Sam is right.