| Exam Board | OCR |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Substitution to find new equation |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring mechanical substitution x=1/u (multiply through by u³) and then applying standard symmetric function relationships. Part (ii) follows directly from recognizing the required expression as a ratio of elementary symmetric functions from the transformed equation. While it's Further Maths content, the technique is routine and well-practiced. |
| Spec | 4.05b Transform equations: substitution for new roots |
3 The cubic equation $2 x ^ { 3 } - 3 x ^ { 2 } + 24 x + 7 = 0$ has roots $\alpha , \beta$ and $\gamma$.\\
(i) Use the substitution $x = \frac { 1 } { u }$ to find a cubic equation in $u$ with integer coefficients.\\
(ii) Hence, or otherwise, find the value of $\frac { 1 } { \alpha \beta } + \frac { 1 } { \beta \gamma } + \frac { 1 } { \gamma \alpha }$.
\hfill \mbox{\textit{OCR FP1 2008 Q3 [4]}}