Let [math]{\small f(x) = x^3 + c_2 x^2 + c_1 x + c_0, }[/math] where
[list=1]
[*][math]{\small f'(a) = f'(b) = 0,} \;\;\;\;\;\; a, b[/math] real; [math] \;\;\; a \ne b.[/math]
[/list]
Then f(x) has at least one root given by a continued fraction.
Demonstration of the case f(b) <0, (and therefore a root r > b.)
_________
The Cubic Equation: [url]http://www.geogebratube.org/student/b143433#chapter/4603[/url]
