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 Linear and quadratic (Posted on 2007-10-23)
Solve bx + c = 0 for x by means of the quadratic formula.

 See The Solution Submitted by Kurious Rating: 3.0000 (3 votes)

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 No Subject | Comment 4 of 9 |

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.

 Posted by Charlie on 2007-10-23 14:54:06

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