| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Show discriminant inequality, then solve |
| Difficulty | Moderate -0.5 This is a standard discriminant question requiring routine application of b²-4ac > 0 for distinct real roots, followed by solving a quadratic inequality. The algebra is straightforward (rearranging to standard form, expanding the discriminant condition, factoring k²-2k-24). Slightly easier than average because it's a well-practiced technique with clear steps and the 'show that' in part (a) provides the target expression. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable |
8. The equation
$$( k + 3 ) x ^ { 2 } + 6 x + k = 5 , \text { where } k \text { is a constant, }$$
has two distinct real solutions for $x$.
\begin{enumerate}[label=(\alph*)]
\item Show that $k$ satisfies
$$k ^ { 2 } - 2 k - 24 < 0$$
\item Hence find the set of possible values of $k$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 Q8 [7]}}