| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 4 |
| Topic | Discriminant and conditions for roots |
| Type | Find range for two distinct roots |
| Difficulty | Moderate -0.3 This is a standard discriminant problem requiring students to apply b²-4ac ≥ 0 for real roots and solve a quadratic inequality. It's slightly easier than average because it's a routine application of a well-practiced technique with straightforward algebra, though the inequality solving adds a small step beyond pure recall. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions |
It is given that
$$f(x) = x^2 - kx + (k+3),$$
where $k$ is a constant.
If the equation $f(x) = 0$ has real roots find the range of the possible values of $k$. [4]
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q11 [4]}}