40. It is easy to check that f(r) =r² – 4x has two roots. Find these two roots using %3D Newton's method In+1 = In - f(rn)/f'(In). (11) If you can find only one root, explain why? [Hint: First write the Newton's iteration formula, then use different initial values xo = 1 and then xo = -1 to see if you can get two different roots.]

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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40. It is easy to check that f(x) = x² – 4x has two roots. Find these two roots using
Newton's method
In+1 = Xn - f(In)/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
xo = 1 and then ro = -1 to see if you can get two different roots.]
Transcribed Image Text:40. It is easy to check that f(x) = x² – 4x has two roots. Find these two roots using Newton's method In+1 = Xn - f(In)/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 xo = 1 and then ro = -1 to see if you can get two different roots.]
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