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Then the equation $\map f x = 0$ is the general quintic equation over $\mathbb k$.
The quintic equation:
- $z^5 - 2 z^4 - z^3 + 6 z - 4 = 0$
- $1, 1, 2, -1 \pm i$
- Abel-Ruffini Theorem, which proves that, in general, a quintic equation can not be solved analytically.