| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Quadratic with equal roots |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing standard completing the square technique and understanding of equal roots (discriminant = 0). Part (a) is a routine algebraic manipulation with clear steps, and part (b) requires only substituting the equal roots condition into the result from part (a). Both parts are textbook exercises requiring recall and basic application rather than problem-solving. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points |
\begin{enumerate}[label=(\alph*)]
\item Prove, by completing the square, that the roots of the equation $x^2 + 2kx + c = 0$, where $k$ and $c$ are constants, are $-k \pm \sqrt{k^2 - c}$.
[4]
\end{enumerate}
The equation $x^2 + 2kx + 81 = 0$ has equal roots.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the possible values of $k$.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q3 [6]}}