11. (a) On Diagram 1 sketch the graphs of
- \(y = x ( 3 - x )\)
- \(y = x ( x - 2 ) ( 5 - x )\)
showing clearly the coordinates of the points where the curves cross the coordinate axes.
(b) Show that the \(x\) coordinates of the points of intersection of
$$y = x ( 3 - x ) \text { and } y = x ( x - 2 ) ( 5 - x )$$
are given by the solutions to the equation \(x \left( x ^ { 2 } - 8 x + 13 \right) = 0\)
The point \(P\) lies on both curves. Given that \(P\) lies in the first quadrant,
(c) find, using algebra and showing your working, the exact coordinates of \(P\).
\includegraphics[max width=\textwidth, alt={}]{c8f8d35d-c2dd-4a1f-a4bb-a4fa06413d12-23_824_1211_296_370}
\section*{Diagram 1}