Solve bx + c = 0 for x by means of the quadratic formula.
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.
-b +/- (b^2 - 4ac)^(1/2)
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.
Posted by Charlie
on 2007-10-23 14:54:06