| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2024 |
| Session | October |
| Marks | 6 |
| Topic | Discriminant and conditions for roots |
| Type | Show discriminant inequality, then solve |
| Difficulty | Moderate -0.3 This is a straightforward discriminant problem requiring rearrangement to standard form, applying b²-4ac < 0, and solving a quadratic inequality. While it involves multiple steps (6 marks total), each step follows standard A-level procedures with no novel insight required. The algebraic manipulation is routine, 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 $kx^2 + 2kx + 2k = 3x - 1$, where $k$ is a constant, has no real roots.
\begin{enumerate}[label=(\alph*)]
\item Show that $k$ satisfies the inequality
$$4k^2 + 16k - 9 > 0.$$ [4]
\item Hence find the set of possible values of $k$. Give your answer in set notation. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2024 Q4 [6]}}