| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Equation with linearly transformed roots |
| Difficulty | Standard +0.8 This is a Further Maths question requiring systematic application of root transformation techniques. Students must use relationships between roots and coefficients, then construct a new equation through substitution y = 2x + 1. While the method is standard for FP1, it requires careful algebraic manipulation across multiple steps and is more demanding than typical A-level pure maths questions. |
| Spec | 4.05b Transform equations: substitution for new roots |
The roots of the cubic equation $2x^3 - 3x^2 + x - 4 = 0$ are $\alpha$, $\beta$ and $\gamma$.
Find the cubic equation whose roots are $2\alpha - 1$, $2\beta - 1$ and $2\gamma - 1$, expressing your answer in a form with integer coefficients. [7]5 The roots of the cubic equation $2 x ^ { 3 } - 3 x ^ { 2 } + x - 4 = 0$ are $\alpha , \beta$ and $\gamma$.\\
Find the cubic equation whose roots are $2 \alpha + 1,2 \beta + 1$ and $2 \gamma + 1$, expressing your answer in a form with integer coefficients.
\hfill \mbox{\textit{OCR MEI FP1 2007 Q5 [7]}}