Finding remaining zeros of linear phase FIR filter
For linear phase FIR filters, each zero at z = z0 will have a matching reciprocal zero at z = 1/zo. And for real-valued coefficients each zero at z = zo will have a matching conjugate zero at z = *zo. Thus for linear phase real-valued coefficients, when you place one zero on the z-plane you determine the location of the other three zeros.