| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Complex roots with real coefficients |
| Difficulty | Moderate -0.8 This is a straightforward application of the complex conjugate root theorem for polynomials with real coefficients, followed by routine use of Vieta's formulas or expansion. It requires only direct recall of standard theory with minimal calculation, making it easier than average even for Further Maths. |
| Spec | 4.02g Conjugate pairs: real coefficient polynomials |
2. Given that $- 2 + 3 \mathrm { i }$ is a root of the equation
$$z ^ { 2 } + p z + q = 0$$
where $p$ and $q$ are real constants,
\begin{enumerate}[label=(\alph*)]
\item write down the other root of the equation.
\item Find the value of $p$ and the value of $q$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2014 Q2 [4]}}