| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Roots with special relationships |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question using symmetric roots and Vieta's formulas. The symmetric form a-d, a, a+d immediately gives the sum of roots = 3a = 3 (from coefficient of x²), so a=1. Then using product of roots gives d, and finally the middle coefficient gives k. It's mechanical application of standard techniques with no novel insight required, making it slightly easier than average even for FM. |
| Spec | 4.05a Roots and coefficients: symmetric functions |
3 The roots of the cubic equation $4 x ^ { 3 } - 12 x ^ { 2 } + k x - 3 = 0$ may be written $a - d , a$ and $a + d$. Find the roots and the value of $k$.
\hfill \mbox{\textit{OCR MEI FP1 2010 Q3 [6]}}