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\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{618d118a-2557-42f3-9b55-4a55dda93a97-1_449_376_631_889}
\captionsetup{labelformat=empty}
\caption{Fig. 13}
\end{figure}
Fig. 13 shows a sketch of the curve \(y = \mathrm { f } ( x )\), where \(\mathrm { f } ( x ) = x ^ { 3 } - 5 x + 2\).
- Use the fact that \(x = 2\) is a root of \(\mathrm { f } ( x ) = 0\) to find the exact values of the other two roots of \(\mathrm { f } ( x ) = 0\), expressing your answers as simply as possible.
- Show that \(\mathrm { f } ( x - 3 ) = x ^ { 3 } - 9 x ^ { 2 } + 22 x - 10\).
- Write down the roots of \(\mathrm { f } ( x - 3 ) = 0\).