given the polynomial p(x) and 3+5i a solution, then so is the number?

Answer 1

Please specify p(x).

EDIT: one assumption could be that p(x) has "real coefficients". Then and only then could the other answerer's be right in calling the conjugate an implicit answer.

Answer 2

If 3 + 5i is a solution to a polynomial, then 3 - 5i will also be a solution. They are called complex conjugates, because they are complex numbers and when they are solutions to polynomials, they will show up in pairs.

Answer 3

Regardless of p(x), if 3+5i is a solution then so is its conjugate, 3-5i.