Show that if h[n] is an N-point FIR filter such that h[n] = h[N 1

Question:

Show that if h[n] is an N-point FIR filter such that h[n] = h[N – 1 – n] and H(z₀) = 0, then H(1/z₀) = 0. This shows that even symmetric linear-phase FIR filters have zeros that are reciprocal images. (If h[n] is real, the zeros also will be real or will occur in complex conjugates.)