| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Find k for equal roots |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic quadratic factorization and the discriminant condition for equal roots. Part (a) is simple factorization (factoring out 4x), and part (b) requires setting b²-4ac=0 and solving, which is direct application of a standard formula with no problem-solving insight needed. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown |
\begin{enumerate}
\item (a) Solve the equation $4 x ^ { 2 } + 12 x = 0$.
\end{enumerate}
You are given that $\mathrm { f } ( x ) = 4 x ^ { 2 } + 12 x + c$, where $c$ is a constant.\\
(b) Given that $\mathrm { f } ( x ) = 0$ has equal roots, find the value of $c$ and hence solve $\mathrm { f } ( x ) = 0$.\\
\hfill \mbox{\textit{Edexcel C1 Q1 [7]}}