1 The equation
$$x ^ { 3 } - x ^ { 2 } + 4 x - 900 = 0$$
has exactly one real root, \(\alpha\).
Taking \(x _ { 1 } = 10\) as a first approximation to \(\alpha\), use the Newton-Raphson method to find a second approximation, \(x _ { 2 }\), to \(\alpha\). Give your answer to four significant figures.
(3 marks)
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