| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete square then solve equation |
| Difficulty | Moderate -0.8 This is a straightforward completing the square exercise with routine algebraic manipulation. Part (a) requires standard completion technique (a=-4, b=-45), and part (b) is a direct application of solving from completed square form. Both parts follow textbook procedures with no problem-solving insight required, making it easier than average but not trivial due to the two-part structure and algebraic care needed. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.02e Complete the square: quadratic polynomials and turning points |
$x^2 - 8x - 29 = (x + a)^2 + b$,
where $a$ and $b$ are constants.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $a$ and the value of $b$. [3]
\item Hence, or otherwise, show that the roots of
$$x^2 - 8x - 29 = 0$$
are $c \pm d\sqrt{5}$, where $c$ and $d$ are integers to be found. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q3 [6]}}