I discovered an elegant theorem. But it is easy to prove using some heavy altirary.

Theorem:Let $\displaystyle f(x)$ be a polynomial with rational coefficients having a prime degree $\displaystyle p$. If $\displaystyle f(x)$ is irreducible (cannot be factored in terms of other non-constant polynomials having rational coefficients) then $\displaystyle f(x)$ has exactly $\displaystyle p$ complex zeros.