New posts in Splitting Field

Let $f(x)= x^3+ax^2+bx+c \in \mathbb{Q}[x]$. Show that the splitting field of $f$ over $\mathbb{Q}$ has degree 1, 2, 3 or 6 over $\mathbb{Q}$.

Ramification in a splitting field

Find an example about splitting field

An irreducible polynomial in $\mathbb Q[x]$ that has all zeros with multiplicity $2$

Prove that $[\mathbf{Q}(\sqrt{1+i},\sqrt{2}):\mathbf{Q}]=8$.

Degree of splitting field of $X^4+2X^2+2$ over $\mathbf{Q}$

Prove that $[\mathbb{Q}(\sqrt{4+\sqrt{5}},\sqrt{4-\sqrt{5}}):\mathbb{Q}] = 8$.

Finite dimensional central division $\mathbb K$-algebra as a subalgebra of a matrix $\mathbb K$-algebra

Prove $f(x)=x^8-24 x^6+144 x^4-288 x^2+144$ is irreducible over $\mathbb{Q}$

Galois group of an irreducible , separable polynomial be abelian , then each of the roots of the polynomial generates the splitting field?