### Constraints on polynomial coefficients

Given a polynomial P=(X-a)*(X-b)*(X-c) over Q[a,b,c][X] , how can I force the coefficients to fullfill constraints such as elementary symetric function a+b+c=0 or a*b*c=2, some polynomial constraint on coefficients.

It is a bit like using coefficients on a number field with the constraint of a minimal polynomial but with different constraints here.