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\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a94593ca-d84d-4747-ac19-b05389e85b3c-1_781_1462_1118_342}
\captionsetup{labelformat=empty}
\caption{Fig. 12}
\end{figure}
Fig. 12 shows the graph of a cubic curve. It intersects the axes at \(( - 5,0 ) , ( - 2,0 ) , ( 1.5,0 )\) and \(( 0 , - 30 )\).
- Use the intersections with both axes to express the equation of the curve in a factorised form.
- Hence show that the equation of the curve may be written as \(y = 2 x ^ { 3 } + 11 x ^ { 2 } - x - 30\).
- Draw the line \(y = 5 x + 10\) accurately on the graph. The curve and this line intersect at ( \(- 2,0\) ); find graphically the \(x\)-coordinates of the other points of intersection.
- Show algebraically that the \(x\)-coordinates of the other points of intersection satisfy the equation
$$2 x ^ { 2 } + 7 x - 20 = 0$$
Hence find the exact values of the \(x\)-coordinates of the other points of intersection.