Each of the four locations z = 1/2, z = 1/4, z = 0, and z = —1/2 is a single-order pole...

Each of the four locations z = 1/2, z = 1/4, z = 0, and z = —1/2 is a single-order pole or zero of G(z)H(z). Furthermore, G(z)H(z) is known to have only two poles. What information can you deduce about the poles and zeros of G(z)H(z) from the fact that for all K, the root locus corresponding to

is on the real axis.