Let $f=2x^5-5x^4+5\in \Bbb Q[x]$. Then, how to prove that it's not solvable by radicals?
Since $f$ is solvable by radicals iff $Gal(f)$ is solvable and $Gal(f)\subset S_5$ (up to isomorphism), I try to prove that $Gal(f)$ is not solvable, but how to do it?
The roots of $f$ have weird form, so I don't get any information about $Gal(f)$...
Give some hint about it and tip to solve a problem like this: polynomial is solvable by radical or not.