The polynomial $X^3-2$ is Eisenstein over $\mathbb Q_2$, hence irreducible. Its discriminant is $-108=36(-3)$, and $-3\equiv5\pmod8$ is not a square in $\mathbb Q_2$. Therefore its splitting field has Galois group $S_3\cong D_6$.

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Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 136 / 4 / c / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-136/4/c/i/solution