Groups and FieldsChallengeGalois Theory ShareGalois Theory · Challenge problemx5−10x+5x^5-10x+5x5−10x+5 is Eisenstein at 555. Its Galois group has order 120120120. Can its roots be written with radicals?AYes: it is irreducibleBYes: every quintic canCOnly numericallyDNo: its Galois group S5S_5S5 is not solvableCheck Show answer Walk through it step by step Practice more like this Review this concept