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Linear and quadratic (Posted on 2007-10-23) Difficulty: 2 of 5
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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Some Thoughts 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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