I'm having trouble wrapping my head around this, and google has been surprisingly unhelpful. I don't intuitively see why a field being algebraically closed means that every irreducible polynomial over that field must have distinct roots.
[Math] Why is every algebraically closed field perfect
field-theory
Best Answer
Over an algebraically closed field the only irreducible polynomials are those of degree$~1$. They obviously cannot have multiple roots.