| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2024 |
| Session | October |
| Marks | 7 |
| Topic | Discriminant and conditions for roots |
| Type | Find range for no real roots |
| Difficulty | Standard +0.3 This is a standard discriminant problem requiring students to apply b²-4ac < 0 for no real roots, then solve a quadratic inequality. While it involves multiple algebraic steps and careful inequality handling, it's a routine application of a core A-level technique with no novel insight required, making it slightly 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 |
The quadratic equation $kx^2 + (3k - 1)x - 4 = 0$ has no real roots. Find the set of possible values of $k$. [7]
\hfill \mbox{\textit{SPS SPS SM 2024 Q4 [7]}}