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I think I would go with 4 .m files as well. One for secant, newton, bisect, and false position.
In anything relating to code, don't worry to much about what other people are doing. I know it makes you a little nervous when you see someone doing something completely different than the way you are doing it. Just remember, especially with code, there are a ton of different ways to do everything. Just choose a way that makes sense to you.
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