Let x[n] = x[-n]. Let X(z) be the z-transform of x[n]. If 0.5 + j0.25 is a zero of X(z), which one of the following must also be a zero of X(z).

In this case, we are given that $0.5 + j0.25$ is a zero of $X(z)$. Therefore, $z^{-1} = 0.5 – j0.25$ is a pole of $X(z)$. The reciprocal of a pole is a zero, so $1 / (0.5 – j0.25)$ is also a zero of $X(z)$.

The other options are not necessarily zeros of $X(z)$. For example, $0.5 + j0.25$ is not a zero of $X(z)$, since $z^{-1} = 0.5 + j0.25$ is not a pole of $X(z)$.