Finding Roots of a Polynomial in a Given Range

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I want to be able to analyze complicated polynomials (degree $6,7$ etc.) and find out if they have roots in a given range. How do I proceed to do this using Mathematica, Matlab, or analytically(if possible at all)?

Also, how do I prove (or at least convince myself), or disprove if a large polynomial has a unique positive root?

I'm beginning to learn Matlab and Mathematica so I would really appreciate it if you can provide me with a source(s) to learn these things. Thank you!

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