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On 08/26/2010 07:21 PM, ludwik kowalski wrote:
A mathematician would say that each (a,b,c) produces one x, a complex
number. S/he would be interested in distributions or the real and
imaginary parts of x, as clarified yesterday.
OK.
A physicist or engineer, on the other hand, dealing with a specific
case, would have to decide whether or not the imaginary (or
negative-real) solutions make sense. Suppose the x stands for the mass
of an object. In that case negative solutions would be ignored.
On the other hand, suppose we have a quadratic
where the variable is a wave vector. In that case
the positive solution make sense, the negative
solutions make sense, and at least one branch of
the complex solutions make sense.
Similarly, suppose we have a quadratic where the
variable is an impedance in an electronic circuit.
All four segments of the "pitchfork" make sense in
some cases.
Negative numbers and complex numbers do not belong
to the mathematicians to the exclusion of physicists
and engineers.
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