Question
Let $f(x)$ be a nonconstant element of $F[x] .$ If $a$ belongs to some extension of $F$ and $f(a)$ is algebraic over $F$, prove that $a$ is algebraic over $F$.
Step 1
Since $f(x)$ is nonconstant, its degree is at least 1. Let $n = \deg(f(x))$. Show more…
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