Alg_Complete

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Unformatted text preview: his way the term x - 5 shows up twice and each term gives the same zero, x = 5 . Saying that the multiplicity of a zero is k is just a shorthand to acknowledge that the zero will occur k times in the list of all zeroes. Example 2 List the multiplicities of the zeroes of each of the following polynomials. (a) P ( x ) = x 2 + 2 x - 15 (b) P ( x ) = x 2 - 14 x + 49 (c) P ( x ) = 5 x5 - 20 x 4 + 5 x3 + 50 x 2 - 20 x - 40 = 5 ( x + 1) ( x - 2) 3 (d) Q ( x ) = x8 - 4 x 7 - 18 x 6 + 108 x5 - 135 x 4 = x 4 ( x - 3) ( x + 5 ) 3 2 (e) R ( x ) = x 7 + 10 x 6 + 27 x5 - 57 x3 - 30 x 2 + 29 x + 20 = ( x + 1) ( x - 1) ( x + 5 )( x - 4 ) © 2007 Paul Dawkins 251 2 3 http://tutorial.math.lamar.edu/terms.aspx College Algebra Solution We’ve already determined the zeroes of each of these in previous work or examples in this section so we won’t redo that work. In each case we will simply write down the previously found zeroes and then go back to the factored form of the polynomial, look at the exponent on each term and give the multiplicity....
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## This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.

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