If $f(x) \in \Bbb C[x]$ is a non constant irreducible polynomial, then what are the possible degrees of $f(x)$? What if $f(x)$ is in $\Bbb R[x]$?
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One. That's D'Alembert-Gauß' theorem. – Bernard Dec 09 '19 at 23:07
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In $\mathbb C[x]$: it's degree 1, and in $\mathbb R[x]$: it's degree 1 and 2. – Dave Dec 09 '19 at 23:25