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I've recently retired and it has been a very long time since I was exposed to a classroom learning about quadratic equations. But now finally jobless, I have more time to satisfy some personal curiousities. For my difficulty in not being able to ask a more sensible question, I apologise in advance. I do hope to get better at it.

I seem to remember that quadratic solutions often resulted in more than one set of coordinates. The root sets might not seem related (quantity/ratio-wise) and it also seems we just merrily threw some of these sets away because, on the surface, they just didn't make sense. On the other hand, I believe math doesn't lie, and discarding perfectly good numbers seemed to me, wrong in principle then; and it still seems wrong today. All solutions should have some insight value.

Since I also believe math must be firmly based in geometry, we might, therefore, simply throw away a set of assumed-useless coordinates that don't match the expected picture. If this is a true perspective, is there some sort of master rule that states, by some sort of deep reasoning, that some coordinate sets must be derived as incorrect? If no rule applies, has the casual abandonment ever fouled up the intepretation of an answer we should have used, or at least considered?

It does seem as if, choosing the wrong basic set, of the various roots, might arbitrarily result in asymmetries that lead down entirely different paths in searching for reality. As an example, the math might continue to be right on, but the overall interpretation of complicated geometry ratios could be wrong. Perhaps the story of Galileo and geocentricity vs heliocentricity is an example.

Thanks,

Wes

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# Discarding some quadratic roots - ok?

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