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**Byun** Let $\displaystyle R$ and $\displaystyle S$ be Noetherian integral domain with $\displaystyle R \subset S$. Suppose that $\displaystyle a,b \in S$ are roots of the monic polynomials

$\displaystyle x^2+c_1x+c_0, x^2+d_1x+d_0 \in R[x]$ respectively.

Using Grobner basis techniques, exhibit a monic polynomial that has $\displaystyle a+b$ as a root. Do the same for $\displaystyle ab$.

I know method for computing Grobner basis but I don't know how I use Grobner basis techniques for this problem.

Please, give me some hint.