5.
\includegraphics[max width=\textwidth, alt={}]{de1a3480-0d83-43c2-a5a2-2f117b8a50fd-2_515_771_246_438}
The diagram shows the curve \(y = \mathrm { f } ( x )\) where
$$f ( x ) = 4 + 5 x + k x ^ { 2 } - 2 x ^ { 3 }$$
and \(k\) is a constant.
The curve crosses the \(x\)-axis at the points \(A , B\) and \(C\).
Given that \(A\) has coordinates \(( - 4,0 )\),
- show that \(k = - 7\),
- find the coordinates of \(B\) and \(C\).