| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Factor theorem and finding roots |
| Difficulty | Moderate -0.8 This is a straightforward application of the factor theorem with routine algebraic manipulation. Substituting z=3 is trivial verification, factoring out (z-3) is standard, and solving the resulting quadratic requires only the quadratic formula. The Argand diagram is basic plotting. Despite being Further Maths, this is a textbook exercise requiring only recall and standard techniques with no problem-solving insight. |
| Spec | 4.02j Cubic/quartic equations: conjugate pairs and factor theorem4.02k Argand diagrams: geometric interpretation |
3 (i) Show that $z = 3$ is a root of the cubic equation $z ^ { 3 } + z ^ { 2 } - 7 z - 15 = 0$ and find the other roots.\\
(ii) Show the roots on an Argand diagram.
\hfill \mbox{\textit{OCR MEI FP1 2008 Q3 [7]}}