| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2022 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Symmetric functions of roots |
| Difficulty | Standard +0.8 This is a Further Maths F1 question requiring manipulation of roots using Vieta's formulas across two related equations. Part (a) is routine recall, but parts (b) and (c) require algebraic manipulation of expressions involving α-3/β and β-3/α, finding their sum and product, then solving for A and B. This demands careful algebraic technique and multi-step reasoning beyond standard A-level, though it's a fairly typical Further Maths roots question. |
| Spec | 4.05a Roots and coefficients: symmetric functions |
The quadratic equation
$$Ax^2 + 5x - 12 = 0$$
where $A$ is a constant, has roots $\alpha$ and $\beta$
\begin{enumerate}[label=(\alph*)]
\item Write down an expression in terms of $A$ for
\begin{enumerate}[label=(\roman*)]
\item $\alpha + \beta$
\item $\alpha\beta$
\end{enumerate}
[2]
\end{enumerate}
The equation
$$4x^2 - 5x + B = 0$$
where $B$ is a constant, has roots $\alpha - \frac{3}{\beta}$ and $\beta - \frac{3}{\alpha}$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the value of $A$
[3]
\item Determine the value of $B$
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2022 Q6 [8]}}