| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2024 |
| Session | October |
| Marks | 7 |
| Topic | Inequalities |
| Type | Quadratic equation real roots |
| Difficulty | Standard +0.3 This is a straightforward discriminant problem requiring students to set b²-4ac < 0 and solve the resulting quadratic inequality. While it involves multiple algebraic steps (expanding, factorizing, and considering the coefficient of x²), it's a standard textbook exercise 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 variable |
2. The quadratic equation $k x ^ { 2 } + ( 3 k - 1 ) x - 4 = 0$ has no real roots. Find the set of possible values of $k$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2024 Q2 [7]}}