Subresultants[, , var] generates a list of the principal subresultant coefficients of the polynomials and with respect to the variable var.
The first subresultants of two polynomials and , both with leading coefficient one, are zero when and have common roots.
Subresultants returns a list whose length is Min[Exponent[, var], Exponent[, var]] + 1.
See The Mathematica Book: Section 3.3.4.
See also: Resultant, PolynomialGCD, Eliminate, Minors.