Chapter 8.6, Problem 16E

Each of the polynomials $p\left(x\right)$ in Exercises $15-18$ is irreducible over the given field $F$. Find all zeros of $p\left(x\right)$ in the field $F\left(\alpha \right)$ obtained by adjoining a zero of $p\left(x\right)$ to $F$. (In Exercises $17$ and $18$, $p\left(x\right)$ has three zeros in $F\left(\alpha \right)$.)

$p\left(x\right)=x^2+x+2,F={\mathbb{Z}}_3$