| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Find range for no real roots |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing standard discriminant conditions (b² - 4ac < 0) and completing the square. Both parts require direct application of well-practiced techniques with no problem-solving insight needed, making it easier than average but not trivial due to the algebraic manipulation required. |
| 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 Q4 [7]}}