- #1

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What do the 'two' answers represent. I know one of them always seems reasonable, but the other one is whack (but it probably has some significance).

Can someone give me an example of the significance of 'that other answer.' Use any example.

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- Thread starter WardenOfTheMint
- Start date

- #1

- 13

- 0

What do the 'two' answers represent. I know one of them always seems reasonable, but the other one is whack (but it probably has some significance).

Can someone give me an example of the significance of 'that other answer.' Use any example.

- #2

Borek

Mentor

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- #3

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Sometimes the two solutions are both reasonable. It really depends on the specific problem or application.

If you can give an example of where you saw this come up, we might be able to help with why one answer is unphysical for your particular example.

- #4

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Haha, I like your explaination on that one Borek

- #5

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This is the difference between pure and applied math. The quadratic is good for all values of its variable, but some range of these may not be in a range suitable for use in modelling the real world. This is all about setting the valid boundaries at the outset.

Consider the example of using a Fourier series of sines and cosines to accurately represent a periodic electrical signal waveform. The series is good for variable values -infinity through to +infinity. The variable is 2*pi*frequency. The whole concept of "negative" frequency is meaningless! So we set the limits to this modelling. No solutions involving negative frequency allowed. It happens often!

- #6

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If you graph the equation, you can see why it might have one solution, two solutions, or no solutions/complex solution.

- #7

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You mean something like (x-2)(x-2)=0. I guess I was just trying to illustrate the point, and I did not pay too much attention to being complete and precise.

For WardenOfTheMint, let us be clear that quadratics (or higher order even) equations applied to model any real phenomena involving parabolic (or other order) phenomena can have solutions real, or none, or some of either kind, including duplicates. Some will be meaningless and inappropriate.

For pure math, there is no problem in including them all. For applied math, we have to also apply some common sense. Even so, I am sometimes struck by how far some mathematical abstractions and transforms that appear completely meaningless as applied to modeling real situations, can still be involved in arriving at an accurate applied math expression for real physical stuff.

- #8

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For instance, if you throw a from the edge of a cliff, it is only going to hit the ground once, but if you represent it as a quadratic of time versus height, you will have two mathematical solutions, but since one is going to represent where the rock was

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