 We can easily see that this is so by considering the quadratic formula and a monic polynomial with real coefficients.If the discriminant of such a polynomial is negative, then both roots of the quadratic equation have imaginary parts.In particular, if "b" and "c" are real numbers and "b"2 − 4"c" < 0, all the convergents of this continued fraction "solution" will be real numbers, and they cannot possibly converge to a root of the form "u" + "iv" (where "v" ≠ 0), which does not lie on the real number line.