| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Topic | Discriminant and conditions for roots |
| Type | Find range for two distinct roots |
| Difficulty | Moderate -0.8 This is a straightforward discriminant question requiring students to apply b²-4ac > 0 for real and distinct roots, then solve a simple linear inequality. It's a standard textbook exercise with routine algebraic manipulation and no problem-solving insight required, making it easier than average. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions |
7.
The quadratic equation $3 x ^ { 2 } + 4 x + ( 2 k - 1 ) = 0$ has real and distinct roots.\\
Find the possible values of the constant $k$\\
Fully justify your answer.\\[0pt]
[4 marks]\\
\hfill \mbox{\textit{SPS SPS SM 2021 Q7 [4]}}