| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| 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, then solving a quadratic inequality. While it involves multiple steps (6 marks total), each step follows standard A-level procedures with no novel insight required. Slightly easier than average due to the routine nature of the techniques. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable |
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 FM 2024 Q2 [6]}}