| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Complex Numbers Arithmetic |
| Type | Factored form to roots |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths question requiring routine application of quadratic formula to two factors, then substitution of d=4 and plotting on an Argand diagram. While it involves complex numbers (a Further Maths topic), the techniques are mechanical with no problem-solving insight needed—just careful algebraic manipulation and standard procedures. |
| Spec | 4.02i Quadratic equations: with complex roots4.02k Argand diagrams: geometric interpretation |
5.
$$f ( x ) = \left( 9 x ^ { 2 } + d \right) \left( x ^ { 2 } - 8 x + ( 10 d + 1 ) \right)$$
where $d$ is a positive constant.
\begin{enumerate}[label=(\alph*)]
\item Find the four roots of $\mathrm { f } ( x )$ giving your answers in terms of $d$.
Given $d = 4$
\item Express these four roots in the form $a + \mathrm { i } b$, where $a , b \in \mathbb { R }$.
\item Show these four roots on a single Argand diagram.
\includegraphics[max width=\textwidth, alt={}, center]{d7689f4a-a41e-45be-911b-4a74e81997eb-21_2647_1840_118_111}
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2021 Q5 [7]}}