Roots of a Monic polynomial

Question

My attempt Product of roots=(-1)^n sincep(-1)=0 and given no roots inside the unit disc.Hence no roots outside the unit disc. Then all the roots are on the unit circle. Hence p(2)>0 true, p(3)=0 false. Is p(1)=0

Answer 1

Hint: $\;p(0)=-1$ and $\,\lim_{x \to \infty}p(x) = + \infty\,$ on the real axis, so if $p(1) \ne 0$ there would exist at least one real root either inside $(0,1)$ or in $(1, \infty)$. In the latter case, consider that all the roots are on the unit circle means that $x^n\,p(1/x)$ has all roots on the unit circle as well.