The equation \(2 x ^ { 3 } + x ^ { 2 } - 1 = 0\) has exactly one real root.
Show that, for this equation, the Newton-Raphson formula can be written
$$x _ { n + 1 } = \frac { 4 x _ { n } ^ { 3 } + x _ { n } ^ { 2 } + 1 } { 6 x _ { n } ^ { 2 } + 2 x _ { n } }$$
Using the formula given in part (a) with \(x _ { 1 } = 1\)
find the values of \(x _ { 2 }\) and \(x _ { 3 }\)
Explain why, for this question, the Newton-Raphson method cannot be used with \(x _ { 1 } = 0\)