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This question from my textbook on using the iterative method to find roots of an equation has confused me. I answered the question correctly but part c is the source of my confusion. I know that the answer is that the attempt will fail because you will need to take the square root of a negative number. This is the correct answer in the back of the book.

What has confused me is, where the did minus sign go in the iterative formula for part c? I had thought that whether you are finding a negative or positive root, you use the same formula, yet for the positive root they have omitted the minus sign. Why is that?

I have highlighted the relevant areas green.

Question from my textbook

Thanks very much!

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1 Answer 1

up vote 5 down vote accepted

You cannot find the positive root with the same iteration formula as the negative root, since the result of that formula is always a non-positive number. Both formulas are such that a fixed point of the iteration is (or would be) a solution of the original equation, but that fixed point necessarily has the respective sign. More generally, you can always get an iteration formula (that may or may not have attractive fixed points) from an equation by "solving" it for one occurrence of the variable, but if you perform multi-valued operations in the process (like taking a square root), then you may be excluding some solutions that don't correspond to the choice you make.

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