3.
\includegraphics[max width=\textwidth, alt={}]{4a5e8809-b4f6-4d24-b3f9-741eea5cc450-1_522_919_705_411}
The diagram shows the curve with equation \(y = x ^ { 3 } + a x ^ { 2 } + b x + c\), where \(a , b\) and \(c\) are constants. The curve crosses the \(x\)-axis at the point \(( - 1,0 )\) and touches the \(x\)-axis at the point \(( 3,0 )\).
Show that \(a = - 5\) and find the values of \(b\) and \(c\).