Cubic Polynomial $x^3-2$ is Irreducible Over the Field $\Q(i)$
Problem 399
Prove that the cubic polynomial $x^3-2$ is irreducible over the field $\Q(i)$.
Add to solve later Tagged: quadratic field
Add to solve later Galois Group of the Polynomial $x^2-2$
Problem 230
Let $\Q$ be the field of rational numbers.
(a) Is the polynomial $f(x)=x^2-2$ separable over $\Q$?
(b) Find the Galois group of $f(x)$ over $\Q$.
Add to solve later Two Quadratic Fields $\Q(\sqrt{2})$ and $\Q(\sqrt{3})$ are Not Isomorphic
Problem 99
Prove that the quadratic fields $\Q(\sqrt{2})$ and $\Q(\sqrt{3})$ are not isomorphic.
Add to solve later Determine the Splitting Field of the Polynomial $x^4+x^2+1$ over $\Q$
Problem 92
Determine the splitting field and its degree over $\Q$ of the polynomial
\[x^4+x^2+1.\]
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Add to solve later $x^3-\sqrt{2}$ is Irreducible Over the Field $\Q(\sqrt{2})$
Problem 82
Show that the polynomial $x^3-\sqrt{2}$ is irreducible over the field $\Q(\sqrt{2})$.
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