Breakpoints, poles and zeros of a band reject filter
Corner frequencies are not the poles of the transfer function and hence you wouldn't get value of denominator equal to zero at those frequencies ,these frequencies in some books refer as pole or zeroes but actually they are not !
Poles and Zeroes of a transfer function is decided by real part of 'S' not by imaginary parts of S(i.e frequency part). But for bode plot we already assumed that $$Re[S] =0$$ and so concept of pole Zero doesn't make sense