# Section 4.6: Analysis

Just after my comments on the previous section come the answer to my question. Ends up that “Every nonconstant polynomial in $\mathbb{C} [x]$ has a root in $\mathbb{C}$.”

The last corollary says “Every polynomial f(x) of odd degree in $\mathbb{R} [x]$ has a root in $\mathbb{R}$.” But what about even degree polynomials. It isn’t hard to see, for low even degree polynomials, that there are roots. For what even degree polynomials will there be a root in $\mathbb{R}$?