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Root of the problem

(See attached file for full problem description with proper symbols and equations)

First: solve this problem.
Second: check my answer.
Third: if my answer is wrong or incomplete explain why.

Explain why cannot have more than one root.

This is how I tried to solve it:

I used the interval [-1,1]

By the Intermediate Value Theorem, since f(0) is between (-1,1), f(0) is the only root.