| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Discriminant for real roots condition |
| Difficulty | Moderate -0.3 This is a standard C1 question testing discriminant conditions and completing the square. Part (a) requires knowing b²-4ac<0 for no real roots (routine application), and part (b) is a textbook completing-the-square exercise. Both are well-practiced techniques with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points |
$f(x) = x^2 - kx + 9$, where $k$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Find the set of values of $k$ for which the equation $f(x) = 0$ has no real solutions. [4]
\end{enumerate}
Given that $k = 4$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item express $f(x)$ in the form $(x - p)^2 + q$, where $p$ and $q$ are constants to be found, [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q35 [7]}}