# Grobner Basis and roots of polynomials

Given R and S Noetherian Integral Domains with $R \subset S$, suppose $a,b \in S$ are roots of the monic polynomial $x^2 + c_1x + c_0, x^2 +d_1x +d_0 \in R[x]$ respectively. Using Grobner Basis Techniques, exhibit a monic polynomial that has a and b as a root. Do the same for ab.