| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Show discriminant inequality, then solve |
| Difficulty | Moderate -0.8 This is a straightforward discriminant question requiring standard application of b²-4ac ≥ 0 for real roots, followed by routine inequality solving and identification of the equal roots case (discriminant = 0). All steps are textbook procedures with no novel insight required, making it easier than average but not trivial due to the algebraic manipulation involved. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation |
The equation $x^2 + 5kx + 2k = 0$, where $k$ is a constant, has real roots.
(a) Prove that $k(25k – 8) \geq 0$.
(2)
(b) Hence find the set of possible values of $k$.
(4)
(c) Write down the values of $k$ for which the equation $x^2 + 5kx + 2k = 0$ has equal roots.
(1)2. The equation $x ^ { 2 } + 5 k x + 2 k = 0$, where $k$ is a constant, has real roots.
\begin{enumerate}[label=(\alph*)]
\item Prove that $k ( 25 k - 8 ) \geq 0$.
\item Hence find the set of possible values of $k$.
\item Write down the values of $k$ for which the equation $x ^ { 2 } + 5 k x + 2 k = 0$ has equal roots.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q2 [7]}}