X 1 x2 x3 multiplicity 2 multiplicity 1 multiplicity

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Unformatted text preview: that this fact doesn’t tell us what the zero is, it only tells us that one will exist. Also, note that if both evaluations are positive or both evaluations are negative there may or may not be a zero between them. Here is the process for determining all the rational zeroes of a polynomial. © 2007 Paul Dawkins 265 http://tutorial.math.lamar.edu/terms.aspx College Algebra Process for Finding Rational Zeroes 1. Use the rational root theorem to list all possible rational zeroes of the polynomial P ( x ) . 2. Evaluate the polynomial at the numbers from the first step until we find a zero. Let’s suppose the zero is x = r , then we will know that it’s a zero because P ( r ) = 0 . Once this has been determined that it is in fact a zero write the original polynomial as P ( x) = ( x - r )Q ( x) 3. Repeat the process using Q ( x ) this time instead of P ( x ) . This repeating will continue until we reach a second degree polynomial. At this point we can solve this directly for the remaining zeroes. To simpli...
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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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