Let be the set of all polynomials in the variable x, with coefficients from and the usual operations of addition and multiplication. Let be the set of polynomials in with roots at and . Prove that is a subring of .
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Originally Posted by Aryth Let be the set of all polynomials in the variable x, with coefficients from and the usual operations of addition and multiplication. Let be the set of polynomials in with roots at and . Prove that is a subring of . Do it by definition. For example, for additive closure say . Then since and .
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