For each of the following, if it is true prove it and if it is not true give a specific example for which the statement is false. (a) If r1r1 is a zero of polynomial P1(x)P1(x) and r2r2 is a zero of polynomial P2(x)P2(x), then r1−r2r1−r2 is a zero of polynomial P1(x)−P2(x)P1(x)−P2(x).

For each of the following, if it is true prove it and if it is not true give a specific example for which the statement is false. (a) If r1r1 is a zero of polynomial P1(x)P1(x) and r2r2 is a zero of polynomial P2(x)P2(x), then r1−r2r1−r2 is a zero of polynomial P1(x)−P2(x)P1(x)−P2(x).

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.5: Zeros Of Polynomial Functions

Problem 2SC

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Question

For each of the following, if it is true prove it and if it is not true give a specific example for which the statement is false.

(a) If r1r1 is a zero of polynomial P1(x)P1(x) and r2r2 is a zero of polynomial P2(x)P2(x), then r1−r2r1−r2 is a zero of polynomial P1(x)−P2(x)P1(x)−P2(x).

Consider the polynomial P(x):
(g) Find all zeros of P(x).
4x² + 5x³ - 2x² + 5x - 6.

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