Regula falsi method and Bisection both are :
1) convergent
2)Divrgent
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Newton’s method converges much faster, but has limitations based upon the derivative of the function in question.
The bisection method is slow, but has no limitations and will always get you to the same answer eventually.
The method you use will depend upon whether Newton’s runs into problems with the function in question. In most cases Newton’s is going to be preferable.
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