Abstract Algebra: Theory and Applications · Problem 17.5.5

Integral Domains — Thomas Judson

Mathematics — Abstract Algebra · polynomial-zeros

Problem

Find all of the zeros for each of the following polynomials. ((a)) 5x3+4x2−x+95x^3 + 4x^2 - x + 9 in Z12[x]\mathbb{Z}_{12}[x] ((b)) 3x3−4x2−x+43x^3 - 4x^2 - x + 4 in Z5[x]\mathbb{Z}_5[x] ((c)) 5x4+2x2−35x^4 + 2x^2 - 3 in Z7[x]\mathbb{Z}_7[x] ((d)) x3+x+1x^3 + x + 1 in Z2[x]\mathbb{Z}_2[x] Hint. (a) No zeros in Z12\mathbb{Z}_{12}; (c) 3, 4.

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