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Numerical Methods

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Question 180

The equation x3−3x2+k=0x^3 - 3x^2 + k = 0x3−3x2+k=0, where k>4k>4k>4, has exactly one real root.

a.

Show that, for this equation, the Newton-Raphson formula can be written

xn+1=2xn3−3xn2−k3xn2−6xn x_{n+1} = \frac{2x_n^3 - 3x_n^2 - k}{3x_n^2 - 6x_n} xn+1​=3xn2​−6xn​2xn3​−3xn2​−k​
[3]
b.

Using the formula given in part (a) with x1=−1x_1 = -1x1​=−1, find the values of x2 x_2\,x2​ and x3 x_3\,x3​ in terms of kkk

[2]
c.

Explain why, for this question, the Newton-Raphson method cannot be used with x1=0x_1 = 0x1​=0

[1]
Markscheme

Numerical Methods Questions

  1. A Level
  2. /Maths
  3. /Numerical Methods

329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.

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