If you assume that the poles are -p1 and -p2 then p1+p2 = -a/b and p1 * p2 = 1/b. Since a Miller capacitor splits the poles, we can assume that one of the poles happens at a much higher frequency than the other one. Assume that p1 << p2, then, p1 + p2 will be approximately p2 and we can find the dominant pole p2= -a/b. Having p2, we can use p1 * p2 =1/b to find p1.
If you assume that the poles are -p1 and -p2 then p1+p2 = -a/b and p1 * p2 = 1/b. Since a Miller capacitor splits the poles, we can assume that one of the poles happens at a much higher frequency than the other one. Assume that p1 << p2, then, p1 + p2 will be approximately p2 and we can find the dominant pole p2= -a/b. Having p2, we can use p1 * p2 =1/b to find p1.
Since you know the Miller Theorem, one pole is closer to operating frequency/band, other pole is too far from the other.That's why one is dominant ( you can say that "effective") other one is nonfunctional.