| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete square then solve equation |
| Difficulty | Moderate -0.3 This is a straightforward C1 question testing completing the square and discriminant analysis. Part (a) requires routine algebraic manipulation, part (b) is a simple discriminant proof showing Δ > 0 for all k, and part (c) involves substitution and simplification. While it has multiple parts (8 marks total), each step follows standard procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown |
\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 Q15 [8]}}