Mark each of the following true of false.
___ a. Let F be a field of characteristic 0. A polynomial in F[x] is solvable by radicals if and only if its splitting field in F̅ is contained in an extension of F by radicals.
___ b. Let F be a field of characteristic 0. A polynomial in F[x] is solvable by radicals if and only if its splitting field in F̅ has a solvable Galois group over F.

___ c. The splitting field of x¹⁷ - 5 over Q has a solvable Galois group.
___ d. The numbers π and √π are independent transcendental numbers over Q.
___ e. The Galois group of a finite extension of a finite field is solvable.
___ f. No quintic polynomial is solvable by radicals over any field.
___ g. Every 4th degree polynomial over a field of characteristic 0 is solvable by radicals.
___ h. The zeros of a cubic polynomial over a field F of characteristic 0 can always be attained by means of a finite sequence of operations of addition, subtraction, multiplication, division, and taking square roots starting with elements in F.
____ i. The zeros of a cubic polynomial over a field F of characteristic 0 can never be attained by means of a finite sequence of operations of addition, subtraction, multiplication, division, and taking square roots, starting with elements in F.
___ j. The theory of subnormal series of groups play an important role in applications of Galois theory.