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Which pairs of polynomials f, 9 € C[X] do have exactly one common root? O f- (X - 1), g = (X + X2+X+ 1)2 O - (X - 1), g = (X + X + X+ 1)* O j - x* - 1,g= x + x2 + X +1 %3D O f- X* - 1,g x3+ X2 + X +1

Which pairs of polynomials f, 9 € C[X] do have exactly one common root? O f- (X - 1), g = (X + X2+X+ 1)2 O - (X - 1), g = (X + X + X+ 1)* O j - x* - 1,g= x + x2 + X +1 %3D O f- X* - 1,g x3+ X2 + X +1

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.4: Zeros Of A Polynomial
Problem 1E: 1. Find a monic polynomial of least degree over that has the given numbers as zeros, and a monic...
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Which pairs of polynomials f, 9 € C[X] do have exactly one common root? O f = (X – 1), 9 = (X + X2 + X + 1)2 O f - (X - 1)2, g = (X* + X + X + 1)" O f= x* – 1,g = x + X2 + X +1 O f- X8 - 1, g = X3 + X2 + X +1
Transcribed Image Text:Which pairs of polynomials f, 9 € C[X] do have exactly one common root? O f = (X – 1), 9 = (X + X2 + X + 1)2 O f - (X - 1)2, g = (X* + X + X + 1)" O f= x* – 1,g = x + X2 + X +1 O f- X8 - 1, g = X3 + X2 + X +1
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