 By applying a result obtained by Euler in 1748 it can be shown that the continued fraction solution to the general monic quadratic equation with real coefficients

given by

converges or not depending on both the coefficient "b" and the value of the discriminant, "b"2 − 4"c".If "b" = 0 the general continued fraction solution is totally divergent; the convergents alternate between 0 and formula_18.If "b" ≠ 0 we distinguish three cases.