Applying the quadratic formula directly gives

(-b +/- sqrt(b^2 - 4ac)) /(2a)

which is invalid or indeterminate due to division by zero.

But as a approaches 0 the limit can be found using  l'Hopital's rule.

We have

-b +/- (b^2 - 4ac)^(1/2)
          2a

The derivative of the numerator with regard to a is

+/- 2c(b^2 - 4ac)^(-1/2)

while that of the denominator is 2.

the result is then +/- c/sqrt(b^2) = +/- c/b.

How to tell which to use (+/-) is a problem with this method.