Answered: 2. Let P(x) = ax² + bx + c be an…

2. Let P(x) = ax² + bx + c be an irreducible polynomial in Q[x). Prove that (a) P(x) has two distinct roots; (b) let a and a2 be the two distinct roots of P(x), then a2 is in the number field Q(a1)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 8E: Let be an irreducible polynomial over a field . Prove that is irreducible over for all nonzero ...

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2. Let P(x) = a.x² + bx + c be an irreducible polynomial in Q[x). Prove that
(a) P(x) has two distinct roots;
(b) let a and a2 be the two distinct roots of P(x), then œ, is in the number field Q(a,)

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