| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Quadratic with equal roots |
| Difficulty | Moderate -0.3 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) applies the result directly. While it requires some algebraic fluency, it involves no problem-solving insight and follows predictable textbook patterns, making it slightly easier than average. |
| 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 Q2 [6]}}