| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2021 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Complex roots with real coefficients |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question testing standard knowledge that complex roots come in conjugate pairs for polynomials with real coefficients, followed by routine application of Vieta's formulas or factor theorem. The arithmetic is slightly involved but the conceptual demand is low—it's a direct application of well-rehearsed techniques with no problem-solving insight required. |
| Spec | 4.02i Quadratic equations: with complex roots4.02j Cubic/quartic equations: conjugate pairs and factor theorem |
\begin{enumerate}
\item Given that $x = \frac { 3 } { 8 } + \frac { \sqrt { 71 } } { 8 } \mathrm { i }$ is a root of the equation
\end{enumerate}
$$4 x ^ { 3 } - 19 x ^ { 2 } + p x + q = 0$$
(a) write down the other complex root of the equation.
Given that $x = 4$ is also a root of the equation,\\
(b) find the value of $p$ and the value of $q$.\\
\hfill \mbox{\textit{Edexcel F1 2021 Q2 [5]}}