| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Complex roots with real coefficients |
| Difficulty | Standard +0.3 This is a standard Further Maths question on complex roots with real coefficients. Given one complex root, students use the conjugate root theorem to find another root, then factor to find remaining roots. The Argand diagram is routine plotting. While it requires multiple steps and is Further Maths content, it follows a well-established procedure without requiring novel insight. |
| Spec | 4.02g Conjugate pairs: real coefficient polynomials4.02k Argand diagrams: geometric interpretation |
7.
$$f ( x ) = x ^ { 4 } - 3 x ^ { 3 } - 15 x ^ { 2 } + 99 x - 130$$
\begin{enumerate}[label=(\alph*)]
\item Given that $x = 3 + 2 \mathrm { i }$ is a root of the equation $\mathrm { f } ( x ) = 0$, use algebra to find the three other roots of the equation $\mathrm { f } ( x ) = 0$
\item Show the four roots of $\mathrm { f } ( x ) = 0$ on a single Argand diagram.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2016 Q7 [9]}}