| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Factor theorem and finding roots |
| Difficulty | Moderate -0.5 This is a straightforward application of the factor theorem requiring polynomial division and solving a quadratic. Given one root explicitly, students factor out (2z-3), perform division, then solve the resulting quadratic—all standard techniques with no conceptual challenges beyond routine algebraic manipulation. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
2 You are given that $z = \frac { 3 } { 2 }$ is a root of the cubic equation $2 z ^ { 3 } + 9 z ^ { 2 } + 2 z - 30 = 0$. Find the other two roots.
\hfill \mbox{\textit{OCR MEI FP1 2013 Q2 [6]}}