SandBox
(1)
\begin{align} [K:\mathbb{Q}] \neq card(G) m \leq n Gal([K:k]) x_1,\dotsb,x_n \end{align}
(2)
\begin{align} \Delta \prod_{i=1}^{4} a_i P'(x_i) \end{align}
(3)
\begin{align} \Delta = (-1)^{4*3/2} \prod\limits_{i=1}^{\4} P'(x_i) = \prod (4x_i^3 - 1) = \prod ( 3 + 4/x_i) = \prod (3/x_i)(x_i + 4/3) = -3^4 P(-4/3) = -283$ \end{align}
(4)
\begin{align} x \notin Q \end{align}

$G \hookrightarrow S_{m-1}$

$X+pX+q:=\Delta$

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