10. The equation 2x³ + x² - 1 = 0 has exactly one real root. (a) Show that, for this equation, the Newton-Raphson formula can be written Xn+1 = 4x2 + x² + 1 6x2 + 2xn Using the formula given in part (a) with ₁ = 1 (b) find the values of x2 and 3 (c) Explain why, for this question, the Newton-Raphson method cannot be used with r.
10. The equation 2x³ + x² - 1 = 0 has exactly one real root. (a) Show that, for this equation, the Newton-Raphson formula can be written Xn+1 = 4x2 + x² + 1 6x2 + 2xn Using the formula given in part (a) with ₁ = 1 (b) find the values of x2 and 3 (c) Explain why, for this question, the Newton-Raphson method cannot be used with r.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:10. The equation 2x³ + x² - 1 = 0 has exactly one real root.
(a) Show that, for this equation, the Newton-Raphson formula can be written
4x³ + x² + 1
η
Xn+1 =
6x2 + 2xn
Using the formula given in part (a) with x₁
(b) find the values of x2 and x3
(c) Explain why, for this question, the Newton-Raphson method cannot be used with
x₁ = 0.
2
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