3 The sequence defined by the iterative formula
$$x _ { n + 1 } = \sqrt [ 3 ] { } \left( 17 - 5 x _ { n } \right)$$
with \(x _ { 1 } = 2\), converges to \(\alpha\).
- Use the iterative formula to find \(\alpha\) correct to 2 decimal places. You should show the result of each iteration.
- Find a cubic equation of the form
$$x ^ { 3 } + c x + d = 0$$
which has \(\alpha\) as a root.
- Does this cubic equation have any other real roots? Justify your answer.