Talk:Numerical Methods/Equation Solving

I'm not 100% sure that I've understood the following sentences:
 * An algebraic equation can have at most as many positive roots as the number of changes of sign in $$f(x)$$.
 * An algebraic equation can have at most as many negative roots as the number of changes of sign in $$f(-x)$$.

Taking the first statements as an example - in the simple case of: $$f(x)=(x-1)^2$$, $$f(x)$$ changes it sign $$0$$ times while it has $$2$$ positive solution (which are identical). —Preceding unsigned comment added by Matanbz (discuss • contribs)


 * I believe these comments are meant to apply to coefficients of the polynomials. In the example you give $$f(x)=x^2-2x+1$$ so the coefficients are 1,-2, and 1 and so there are there are two changes in sign. I think this is generally known as Descartes' rule of signs, which gives slightly more info, but the extra information is not so relevant here. Thenub314 (talk) 09:18, 29 May 2010 (UTC)