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 Question from Emily, a student: I have a question about Extraneous Solutions, Because I was recently researching to figure out on how to determine that a solution is extraneous and many of the answers talked about how if a answer is negative that it should always be extraneous but now I found out that positive solutions can also be considered as extraneous solutions so that is why I am really confused Extraneous Solution's. I would really appreciate it if you could clearly explain to me how to determine an extraneous solution from a normal solution. Thanks, Emily

The problem here is that the word “extraneous” has gone out of style; it is used these days, at least in America, almost exclusively in the mathematics classroom. Its use in mathematics is so ingrained that we are stuck with it. Today we would probably say “irrelevant” or “not pertinent” or “not suitable.” For example, negative numbers are irrelevant when dealing with the length of a line segment; thus when you calculate that the correct length can be either plus or minus 5, you would reject the -5 as being irrelevant to your problem (or extraneous in the words of a math teacher). But what is extraneous depends on the context. Thus, when looking up the the word “extraneous” in the dictionary, you will find three definitions, two of which are extraneous in your context. Or in a mathematics problem, you might find a dozen possible values for the quantity you seek, but if you are interested only in the largest value, then the other 11 are extraneous.

Chris

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