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.

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ISBN:9780470458365
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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.
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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