4.
\includegraphics[max width=\textwidth, alt={}, center]{30d4e6e5-8235-44b0-ad8e-c4c0b313677f-1_572_803_1336_461}
The diagram shows the curves with equations \(y = 7 - 2 x - 3 x ^ { 2 }\) and \(y = \frac { 2 } { x }\).
The two curves intersect at the points \(P , Q\) and \(R\).
- Show that the \(x\)-coordinates of \(P , Q\) and \(R\) satisfy the equation
$$3 x ^ { 3 } + 2 x ^ { 2 } - 7 x + 2 = 0$$
Given that \(P\) has coordinates \(( - 2 , - 1 )\),
- find the coordinates of \(Q\) and \(R\).