Root Separation

The root separation (or zero separation) of a polynomial  with roots , , ... is defined by

There are lower bounds on how close two distinct roots of a polynomial can be. In particular, if  is a squarefree polynomial of degree  with discriminant , then the Mahler bound gives the minimum separation distance between any pair of roots as

REFERENCES:

Mahler, K. "An Inequality for the Discriminant of a Polynomial." Michigan Math. J. 11, 257-262, 1964.

Zippel, R. Effective Polynomial Computation. Boston, MA: Kluwer, pp. 186-187, 1993.