| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Quadratic from one complex root |
| Difficulty | Moderate -0.8 This is a standard Further Maths question testing the fundamental property that complex roots of real polynomials come in conjugate pairs, followed by routine application of Vieta's formulas or expansion. While it's FP1 content, it requires only direct recall of theory and basic arithmetic with no problem-solving insight needed. |
| Spec | 4.02g Conjugate pairs: real coefficient polynomials4.02i Quadratic equations: with complex roots |
Given that $2 + i$ is a root of the equation
$$z^2 + bz + c = 0, \text{ where } b \text{ and } c \text{ are real constants,}$$
\begin{enumerate}[label=(\roman*)]
\item write down the other root of the equation,
\item find the value of $b$ and the value of $c$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q4 [5]}}