When approximating the square root of 2 by applying Newton's Method, is the answer (+-)1.4142 or just positive 1.4142?

Question

phi · Answer

generally Newton's method will give you one of the roots, but the other one is the negative of the one found.

zehanz · Answer

I would define this function: f(x) = x²-2.
Differentiating gives f'(x) = 2x.
Newtons method:$$x _{n+1}=\frac{ x _{n}^{2}+2 }{ 2x _{n} }$$

Starting with a positive number for x0, will lead you to 1.4142...
A negative start value goes to -1.4142...

See attached img

babyslapmafro · Answer

Ok, so (+-)1.4142 is a suitable answer to the problem

zehanz · Answer

Yes, it is.