Monday, November 18, 2013

College Algebra, Chapter 4, Chapter Review, Section Review, Problem 58

Find all rational, irrational and complex zeros (and state their multiplicities) of the polynomial function P(x)=18x3+3x24x1. Use Descartes' Rule of signs, the Upper and Lower Bounds Theorem, the Quadratic Formula or other factoring techniques.

The possible rational zeros of P are the factors of 1 divided by the factors of 18 which are ±1,±12,±13,±16,±19 and ±118. Then, by applying Synthetic Division and trial and error,







Again, by applying synthetic division







Thus,


P(x)=18x3+3x24x1=(x+13)(18x23x3)=(x+13)(x+13)(18x9)=(x+13)2(18x9)


Thus, the zeros of P are 13 and 12. The zeros have multiplicity of 2 and 1 respectively.

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