| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete square then solve equation |
| Difficulty | Moderate -0.8 This is a straightforward C1 completing the square question with standard parts: (a) routine algebraic manipulation, (b) simple discriminant argument showing b²-4ac > 0, (c) substitution and simplification. All parts follow textbook procedures with no problem-solving insight required, making it easier than average but not trivial due to the algebraic manipulation with parameter k. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points |
\begin{enumerate}[label=(\alph*)]
\item By completing the square, find in terms of $k$ the roots of the equation
$$x^2 + 2kx - 7 = 0.$$ [4]
\item Prove that, for all values of $k$, the roots of $x^2 + 2kx - 7 = 0$ are real and different. [2]
\item Given that $k = \sqrt{2}$, find the exact roots of the equation. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q4 [8]}}