roots of a polynomial with zero coefficient summation

Question

Consider a polynomial, for which the summation of the coefficients is zero.What do we know about its roots?

Answer 1

If the coeffients of a polynomial $p(x)=\sum p_ix^i$ sum to zero, then $$p(1)=\sum p_i1^i=\sum p_i=0,$$ so $1$ is a root of $p$.