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} ?

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