4. Polynomials.a) Find a monic polynomial in (Z/8Z)[x] with more distinct roots (in Z/8Z) than itsdegree.b) Find a non-0 monic polynomial in (Z/8Z) [x] of degree 4 such that every a € Z/8Zis a root.

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Answered: a) Find a monic polynomial in (Z/8Z)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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a) Find a monic polynomial in (Z/8Z) [x] with more distinct roots (in Z/8Z) than its degree. b) Find a non-0 monic polynomial in (Z/8Z) [x] of degree 4 such that every a € Z/8Z is a root.