| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Show discriminant inequality, then solve |
| Difficulty | Moderate -0.3 This is a standard C1 discriminant question requiring routine application of b²-4ac ≥ 0 for real roots, solving a quadratic inequality, and finding when discriminant equals zero. All steps are textbook procedures with no novel insight required, making it slightly easier than average. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions |
Given that the equation
$$4x^2 - kx + k - 3 = 0,$$
where $k$ is a constant, has real roots,
\begin{enumerate}[label=(\roman*)]
\item show that
$$k^2 - 16k + 48 \geq 0, \quad [2]$$
\item find the set of possible values of $k$, [3]
\item state the smallest value of $k$ for which the roots are equal and solve the equation when $k$ takes this value. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 Q5 [8]}}