| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
2 The roots of the equation
$$x ^ { 3 } + p x ^ { 2 } + q x + r = 0$$
are $\alpha , 2 \alpha , 4 \alpha$, where $p , q , r$ and $\alpha$ are non-zero real constants.\\
(i) Show that
$$2 p \alpha + q = 0$$
(ii) Show that
$$p ^ { 3 } r - q ^ { 3 } = 0$$
\hfill \mbox{\textit{CAIE FP1 2018 Q2}}