| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Given a real root, find complex roots of cubic |
| Difficulty | Standard +0.3 This is a straightforward Further Pure 1 question requiring polynomial division by (z+2), solving a quadratic, plotting on an Argand diagram, and verifying a right angle using distance/dot product. All steps are routine techniques with no novel insight required, making it slightly easier than average even for FP1 standard. |
| Spec | 4.02g Conjugate pairs: real coefficient polynomials4.02i Quadratic equations: with complex roots4.02k Argand diagrams: geometric interpretation |
Given that $-2$ is a root of the equation $z^3 + 6z + 20 = 0$,
\begin{enumerate}[label=(\alph*)]
\item Find the other two roots of the equation, [3]
\item show, on a single Argand diagram, the three points representing the roots of the equation, [1]
\item prove that these three points are the vertices of a right-angled triangle. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q22 [6]}}