6 The following flow chart has been written to find a root of the cubic equation \(x ^ { 3 } + A x ^ { 2 } + B x + C = 0\), given a starting value \(X\) that is thought to be near the root.
\includegraphics[max width=\textwidth, alt={}, center]{ccb12789-cd5f-40dc-9f10-f8bb45399580-8_1410_1648_324_212}

1. Work through the algorithm, recording the values of \(X , Y , Z\) and \(W\) each time they change, for the equation \(x ^ { 3 } - 4 x ^ { 2 } + 5 x + 1 = 0\), with a starting value of \(X = 0\).
2. Show what happens when the algorithm is used for the equation \(x ^ { 3 } - 4 x ^ { 2 } + 5 x + 1 = 0\), with a starting value of \(X = 1\).
3. Show what happens when the algorithm is used for the equation \(x ^ { 3 } - 4 x ^ { 2 } + 5 x + 1 = 0\), with a starting value of \(X = - 1\).
4. Identify a possible problem with using this algorithm.