| 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 -0.3 This is a straightforward C1 question testing standard completing the square technique and understanding of equal roots. Part (a) is a routine algebraic manipulation with clear steps, and part (b) requires recognizing that equal roots means the discriminant equals zero. Both parts are textbook exercises requiring only recall and basic application of standard methods, 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 Q4 [6]}}