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Let Q denote the field of rational numbers, R the field of real numbers, and C the field of complex numbers. Determine whether each of the following polynomials is irreducible over each of the indicated fields, and state all the zeros in each of the fields. x²+2x² + 1 over Z3, Z5, and Z7

Let Q denote the field of rational numbers, R the field of real numbers, and C the field of complex numbers. Determine whether each of the following polynomials is irreducible over each of the indicated fields, and state all the zeros in each of the fields. x²+2x² + 1 over Z3, Z5, and Z7

Advanced Engineering Mathematics
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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Let Q denote the field of rational numbers, R the field of real numbers, and C the field of complex numbers. Determine whether each of the following polynomials is irreducible over each of the indicated fields, and state all the zeros in each of the fields. x²+2x² + 1 over Z3, Z5, and Z7
Transcribed Image Text:Let Q denote the field of rational numbers, R the field of real numbers, and C the field of complex numbers. Determine whether each of the following polynomials is irreducible over each of the indicated fields, and state all the zeros in each of the fields. x²+2x² + 1 over Z3, Z5, and Z7
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