| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Complex roots with real coefficients |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths complex numbers question requiring routine techniques: substitution to verify a root, applying the complex conjugate root theorem, and using sum of roots or polynomial division to find the real root. While it's FP1 content, the methods are standard and mechanical with no problem-solving insight required. |
| Spec | 4.02g Conjugate pairs: real coefficient polynomials4.02i Quadratic equations: with complex roots4.02j Cubic/quartic equations: conjugate pairs and factor theorem |
\begin{enumerate}[label=(\roman*)]
\item Verify that $2 + \mathrm{j}$ is a root of the equation $2x^3 - 11x^2 + 22x - 15 = 0$. [5]
\item Write down the other complex root. [1]
\item Find the third root of the equation. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI FP1 2006 Q8 [10]}}