| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Reciprocal sum of roots |
| Difficulty | Moderate -0.5 This is a straightforward application of Vieta's formulas requiring students to find p+q=-1 and pq=-8, then compute 1/p + 1/q = (p+q)/pq = -1/(-8) = 1/8, giving final answer -1 + 1/8 = -7/8. While it's Further Maths content, it's a routine textbook exercise with clear steps and no novel insight required, making it slightly easier than average. |
| Spec | 4.05a Roots and coefficients: symmetric functions |
4 The roots of the quadratic equation $x ^ { 2 } + x - 8 = 0$ are $p$ and $q$. Find the value of $p + q + \frac { 1 } { p } + \frac { 1 } { q }$.
\hfill \mbox{\textit{OCR FP1 2009 Q4 [4]}}