40. It is easy to check that f(x) = x - 4x has two roots. Find these two roots using Newton's method In+1 = I, - f(xn)/f'(xn). (11) If you can find only one root, explain why? [Hint: First write the Newton's iteration formula, then use different initial values I0 = 1 and then ro =-1 to see if you can get two different roots.
40. It is easy to check that f(x) = x - 4x has two roots. Find these two roots using Newton's method In+1 = I, - f(xn)/f'(xn). (11) If you can find only one root, explain why? [Hint: First write the Newton's iteration formula, then use different initial values I0 = 1 and then ro =-1 to see if you can get two different roots.
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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![40. It is easy to check that f(r) = x² – 4r has two roots. Find these two roots using
Newton's method
Tn+1 = I, - f (xn)/f'(x„).
(11)
If you can find only one root, explain why?
[Hint: First write the Newton's iteration formula, then use different initial values
r0 = 1 and then ro = -1 to see if you can get two different roots.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf585ee5-5848-4008-90f9-765ba6bc4c07%2Ff116bfa3-5703-4913-a4a2-9d4c2a9cfaf5%2Fow6awx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:40. It is easy to check that f(r) = x² – 4r has two roots. Find these two roots using
Newton's method
Tn+1 = I, - f (xn)/f'(x„).
(11)
If you can find only one root, explain why?
[Hint: First write the Newton's iteration formula, then use different initial values
r0 = 1 and then ro = -1 to see if you can get two different roots.
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