An interesting fact about the field $\mathbb{R}$ is that it's halfway to being algebraically closed, inasmuch as every univariate odd degree polynomial with coefficients in $\mathbb{R}$ has a zero. This isn't true of every field. For example, the cubic polynomial $x^3+x+1$ has no zeroes over $\mathbb{F}_2$.
Question. I'd like to learn more. Are there any relevant definitions or notions that an interested reader could search to get more information?