2 Let \(\mathrm { f } ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 4\).
- Show that if a sequence of values given by the iterative formula
$$x _ { n + 1 } = \sqrt { \frac { 4 } { 5 - 2 x _ { n } } }$$
converges, then it converges to a root of the equation \(\mathrm { f } ( x ) = 0\).
- The equation has a root close to 1.2 .
Use the iterative formula from part (a) and an initial value of 1.2 to determine the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.