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Numerical Methods

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Question 101

The equation x3+7x2+4=0x^3 + 7x^2 + 4 = 0x3+7x2+4=0 has exactly one real root.

a.

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

xn+1=2xn3+7xn2−43xn2+14xn x_{n+1} = \frac{2x_n^3 + 7x_n^2 - 4}{3x_n^2 + 14x_n} xn+1​=3xn2​+14xn​2xn3​+7xn2​−4​
[3]
b.

Using the formula given in part (a) with x1=−2x_1 = -2x1​=−2, find the values of x2 x_2\,x2​ and x3x_3x3​

[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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