Let $K$ be any subfield of $\mathbb{C}$ and let $m(t)$ be a quadratic polynomial over $K$. show that all zeros of $m(t)$ lie in an extension $K(\alpha)$ of $K$ where $\alpha^2=k\in K$. Thus allowing square roots $\sqrt k$ enables us to solve all quadratic equations over $K$.
Quadratic polynomial over $K$
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abstract-algebra
polynomials