Question
Let $f(x) \in F[x]$. If deg $f(x)=2$ and $a$ is a zero of $f(x)$ in some extension of $F$, prove that $F(a)$ is the splitting field for $f(x)$ over $F$.
Step 1
Since $f(x)$ has degree 2, it can have at most 2 distinct roots. Let $a$ be one of the roots in some extension of $F$. Show more…
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