| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Quadratic equation real roots |
| Difficulty | Moderate -0.8 This is a straightforward discriminant question requiring students to apply the condition b²-4ac < 0 for no real roots, then solve a simple quadratic inequality by factorization. It's a standard C1 exercise with routine steps and no conceptual challenges, making it easier than average. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation |
5. Given that the equation
$$x ^ { 2 } + 4 k x - k = 0$$
has no real roots,\\
(i) show that
$$4 k ^ { 2 } + k < 0 ,$$
(ii) find the set of possible values of $k$.\\
\hfill \mbox{\textit{OCR C1 Q5 [6]}}