| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Quadratic with transformed roots |
| Difficulty | Standard +0.8 This is a Further Maths question requiring systematic application of Vieta's formulas and algebraic manipulation to find sums/products of transformed roots. Part (a) uses standard identities (α²+β² and α³+β³), while part (b) requires finding sum and product of (α²+β) and (β²+α), which demands careful algebraic work but follows established techniques. More challenging than typical A-level questions due to the multi-step reasoning and algebraic complexity, but still a standard Further Maths exercise. |
| Spec | 4.05a Roots and coefficients: symmetric functions4.05b Transform equations: substitution for new roots |
| VIAV SIHI NI BIIIM ION OC | VGHV SIHI NI GHIYM ION OC | VJ4V SIHI NI JIIYM ION OC |
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\item The quadratic equation
\end{enumerate}
$$2 x ^ { 2 } + 4 x - 3 = 0$$
has roots $\alpha$ and $\beta$.\\
Without solving the quadratic equation,\\
(a) find the exact value of\\
(i) $\alpha ^ { 2 } + \beta ^ { 2 }$\\
(ii) $\alpha ^ { 3 } + \beta ^ { 3 }$\\
(b) Find a quadratic equation which has roots ( $\alpha ^ { 2 } + \beta$ ) and ( $\beta ^ { 2 } + \alpha$ ), giving your answer in the form $a x ^ { 2 } + b x + c = 0$, where $a , b$ and $c$ are integers.
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VIAV SIHI NI BIIIM ION OC & VGHV SIHI NI GHIYM ION OC & VJ4V SIHI NI JIIYM ION OC \\
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\hfill \mbox{\textit{Edexcel F1 2018 Q9 [9]}}