Let F have characteristic 0 and suppose the coefficients of the polynomial

f(x)=a_n x^n + a_(n-1) x^(n-1) + ... + a_1 t + a_{0}

be in F[x] and satisfy a_n=1, a_i = a_(n-i) for all i=0,...,n

(forexample f(t)=t^3-4t^2-4t+1

Show that if f(t) is irredicuble then n is even.

and if n=2k>4,then the galois group of this polynomial (over F) cannot be isomorphic S_n (the symmetric group)