| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Reciprocal sum of roots |
| Difficulty | Moderate -0.8 This is a straightforward application of Vieta's formulas requiring students to recognize that α/β + β/α = (α² + β²)/(αβ), then use sum and product of roots. It's a standard Further Maths exercise with clear technique and minimal steps, making it easier than average even for FM students. |
| Spec | 4.05a Roots and coefficients: symmetric functions |
\begin{enumerate}
\item The quadratic equation
\end{enumerate}
$$3 x ^ { 2 } - 5 x + 1 = 0$$
has roots $\alpha$ and $\beta$.\\
Without solving the quadratic equation, find the exact value of
$$\frac { \alpha } { \beta } + \frac { \beta } { \alpha }$$
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\end{center}
Count coution\\
$\_\_\_\_$ T\\
\hfill \mbox{\textit{Edexcel F1 2017 Q1 [4]}}