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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.3: Quadratic Equations
Problem 82E
Related questions
Question
![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
-
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa16ba84c-9153-4f60-a220-312e73d5be44%2Ff2394aa2-c91c-4808-a590-ce6d1b16b864%2Fjl59j5_processed.jpeg&w=3840&q=75)
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
-
1
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