A question on Newton's Method

Hi, I know this may seem very like a very simple question, but I'm
just a second year physics student and I'm trying to just get ahead
in the game by doing my own work. So to test out my programming
abilities, I built a simple (well it used to be) program that
determines if and when two objects moving along a line will collide. I
was using the quadratic equation to find the roots. The thing is when
I was discussing my little project on the FORTRAN group (FORTRAN is the
language I'm using since its easier then some of the others out
there), someone pointed out that using the quadratic equation is not
exactly stable when it comes to computers. So doing some looking
around I found a book called "Applied Numerical Methods" that showed
how Newton's Method worked. But it's a bit vauge since its meant for
someone a bit more advanced then I am (I'm in Calc 2).

My question is using a guess(X sub 0), will that find the first or
second root? And where should it be, to the left or the right of the
root? And could I use the numbers the quadratic equation gives as my
guess? Also what is the difference between X sub k and X sub k+1? I
know k is the number of iterations, so would that make X sub k+1 my
solution?

Thanks
David M

.

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