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This question is a continuation of Is every polynomial a factor of a trinomial?

We say that $T(X) \in \mathbb{Q}[X]$ is a trinomial if there exist $A,B,C \in \mathbb{Q}$ such that $T(X) = AX^n + BX^m + C$ for some $n \geq m \in \mathbb{N}$.

Let $L$ be the splitting field over $\mathbb{Q}$ of all trinomials. Is $L$ algebraically closed?

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