 Continued fractions are most conveniently applied to solve the general quadratic equation expressed in the form of a monic polynomial

which can always be obtained by dividing the original equation by its leading coefficient.Starting from this monic equation we see that

But now we can apply the last equation to itself recursively to obtain

If this infinite continued fraction converges at all, it must converge to one of the roots of the monic polynomial "x"2 + "bx" + "c" = 0.Unfortunately, this particular continued fraction does not converge to a finite number in every case.