So since we know that x 2 is a zero of p x x3 2 x

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Unformatted text preview: ve also got a product of three terms in this polynomial. However, since the first is now an x this will introduce a third zero. The zeroes for this polynomial are, x = -5, x = 0, and x = 3 because each of these will make one of the terms, and hence the whole polynomial, zero. (c) 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 ) 3 2 With this polynomial we have four terms and the zeroes here are, x = -5, x = -1, x = 1, and x = 4 Now, we’ve got some terminology to get out of the way. If r is a zero of a polynomial and the exponent on the term that produced the root is k then we say that r has multiplicity k. Zeroes with a multiplicity of 1 are often called simple zeroes. For example, the polynomial P ( x ) = x 2 - 10 x + 25 = ( x - 5 ) will have one zero, x = 5 , and its 2 multiplicity is 2. In some way we can think of this zero as occurring twice in the list of all zeroes since we could write the polynomial as, P ( x ) = x 2 - 10 x + 25 = ( x - 5 ) ( x - 5 ) Written t...
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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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