| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2025 |
| Session | November |
| Marks | 5 |
| Topic | Discriminant and conditions for roots |
| Type | Find range for two distinct roots |
| Difficulty | Standard +0.3 This is a discriminant problem requiring students to apply b²-4ac > 0 for two distinct real roots, then solve a quadratic inequality. It's slightly easier than average because it's a standard technique with straightforward algebra, though the inequality solving adds a small challenge beyond basic recall. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions |
The equation $kx^2 + 4x + (5 - k) = 0$, where $k$ is a constant, has 2 different real solutions for $x$.
Find the set of possible values of $k$.
Write your answer using set notation. [5]
\hfill \mbox{\textit{SPS SPS SM 2025 Q3 [5]}}