Does the set of solutions to quadratics over $\mathbb{Q}$ form a subgroup of the additive group $\mathbb{R}$?
2026-04-30 02:03:42.1777514622
Set of solutions to quadratics over $\mathbb{Q}$
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No, because it is not closed under addition. For example, $\sqrt{2}$ and $\sqrt{3}$ are solutions to quadratics, but $\mathbb{Q}(\sqrt{2}+\sqrt{3})=\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a degree 4 extension of $\mathbb{Q}$, and therefore $\sqrt{2}+\sqrt{3}$ is not a solution to a quadratic.