9. Let Zs is a ring of integers mod 5 and f(x)eZs(x) such that f(x) = x²+x+1, then:a)25/f(x) is a field.b) f(x) has only two roots.c) f(x) has more than two roots.d) No one of the above.55

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Answered: 9. Let Zs is a ring of integers mod 5…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 14E

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9. Let Zs is a ring of integers mod 5 and f(x)eZ,(x) such that f(x) = x²+x+1, then: Zs a) f(x) is a field. b) f(x) has only two roots. c) f(x) has more than two roots. d) No one of the above. 55 4