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