zero separation

The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Δ(P) = min_(i!=j) left bracketing bar r_i - r_j right bracketing bar . There are lower bounds on how close two distinct roots of a polynomial can be. In particular, if P(x) is a squarefree polynomial of degree d with discriminant D, then the Mahler bound gives the minimum separation distance between any pair of roots as Δ(p)>sqrt((3 left bracketing bar D right bracketing bar )/d^(d + 2)) left double bracketing bar p right double bracketing bar _2^(1 - d).

polynomial discriminant | root