| Exam Board | WJEC |
|---|---|
| Module | Further Unit 1 (Further Unit 1) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Given one complex root of cubic or quartic, find all roots |
| Difficulty | Standard +0.3 This is a standard further maths question on complex roots of polynomials with real coefficients. Students must recall that complex roots come in conjugate pairs, then perform polynomial division (twice) to find the remaining quadratic, followed by solving it. While it requires multiple steps, each is routine for further maths students with no novel insight needed. |
| Spec | 4.02g Conjugate pairs: real coefficient polynomials4.02j Cubic/quartic equations: conjugate pairs and factor theorem |
3. Given that $5 - \mathrm { i }$ is a root of the equation $x ^ { 4 } - 10 x ^ { 3 } + 10 x ^ { 2 } + 160 x - 416 = 0$,
\begin{enumerate}[label=(\alph*)]
\item write down another root of the equation,
\item find the remaining roots.
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 1 2023 Q3 [6]}}