ring theory Let F be a commutative ring with identity and let f(x) E F[x] be apolynomial of degree 6. Which of the following statements is true:f(x) has exactly 6 roots countingmultiplicity.O f(x) has exactly 6 distinct rootsO f(x) has at most 6 roots.None

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Answered: Let F be a commutative ring with…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 18E: 18. Let be a commutative ring with unity, and let be the principal ideal in . Prove that is...

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Let F be a commutative ring with identity and let f(x) E F[x] be a polynomial of degree 6. Which of the following statements is true: f(x) has exactly 6 roots counting multiplicity. O f(x) has exactly 6 distinct roots O f(x) has at most 6 roots. None