One root as a continued fraction

Let [math]{\small f(x) = x^3 + c_2 x^2 + c_1 x + c_0, }[/math] where [br][list=1][br][*][math]{\small f'(a) = f'(b) = 0,} \;\;\;\;\;\; a, b[/math] real; [math] \;\;\; b>a.[/math][br][*][math]{\small f(b) < 0 }[/math][br][br]Then f(x) has a root r > b given by the following recursion
One root as a continued fraction

Information: One root as a continued fraction