| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Complex roots with real coefficients |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question on complex roots. Given one complex root of a polynomial with real coefficients, students use the conjugate root theorem to find a second root, then perform polynomial division to find a quadratic factor, and solve for the remaining roots. The Argand diagram part is routine plotting. While it requires multiple steps, each step follows standard procedures taught in F1 with no novel insight required, making it slightly easier than average. |
| Spec | 4.02i Quadratic equations: with complex roots4.02j Cubic/quartic equations: conjugate pairs and factor theorem4.02k Argand diagrams: geometric interpretation |
2.
$$f ( z ) = z ^ { 4 } - 6 z ^ { 3 } + 38 z ^ { 2 } - 94 z + 221$$
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\item Given that $z = 2 + 3 i$ is a root of the equation $f ( z ) = 0$, use algebra to find the three other roots of $f ( z ) = 0$
\item Show the four roots of $\mathrm { f } ( \mathrm { z } ) = 0$ on a single Argand diagram.
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\hfill \mbox{\textit{Edexcel F1 2018 Q2 [9]}}