Conjugate reciprocal pairs of zeros and poles in FIR design
Look up the complex conjugate root theorem which states that:


  If all the coefficients of a polynomial are real then its roots are either real or if there is a complex root, then its conjugate is also a root.


This theorem can be applied to the denomerator and numerator of a rational transfer function to judge about its poles and zeros.

"conjugate reciprocal roots" is not a necessary consequence of real coefficients. conjugate reciprocal pole-zeros are considered when we need some specific features such as being all-pass or when designing minimum-phase filters. This is because for instance reflection of a zero to its conjugate reciprocal does not influence on the magnitude response.