| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Factor theorem and finding roots |
| Difficulty | Standard +0.3 This is a straightforward Further Pure question where two roots are given, requiring factorization of a quartic into (x+4)(x-3) times a quadratic, then solving that quadratic. Part (b) is routine plotting on an Argand diagram. While it's Further Maths content, the algebraic manipulation is mechanical and the question provides significant scaffolding by giving two roots explicitly. |
| Spec | 4.02j Cubic/quartic equations: conjugate pairs and factor theorem4.02k Argand diagrams: geometric interpretation |
4.
$$f ( x ) = x ^ { 4 } + 3 x ^ { 3 } - 5 x ^ { 2 } - 19 x - 60$$
\begin{enumerate}[label=(\alph*)]
\item Given that $x = - 4$ and $x = 3$ are roots of the equation $\mathrm { f } ( x ) = 0$, use algebra to solve $\mathrm { f } ( x ) = 0$ completely.
\item Show the four roots of $\mathrm { f } ( x ) = 0$ on a single Argand diagram.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2014 Q4 [9]}}