What is the highest degree this polynomial can have?

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Let P be a polynomial and its coeficiants are 1 or -1. and all roots are real number. What is the highest degree this polynomial can have?

By the integer root theorem. $\pm1$ maybe a root.

I think smth may be wrong with the problem. I mean if k is an odd number $x^k-x^{k-1}+x^{k-2}-...x^2+x-1$ polynomial has only root 1? Edit:my example fails I guess. there are k-1 complex roots