jmc

By considering the expression $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ for the roots of $a{x}^2+bx+c$, we find that the roots are real and distinct if and only if the discriminant $b^2-4ac$ is positive. So the roots of $2x^2+mx+8$ are real and distinct when $m^2-4(2)(8)>0$. Simplifying and factoring the left-hand side, we find $(m-8)(m+8)>0$, which implies $m\in \boxed{(-\infty ,-8)\cup (8,\infty )}$.