If there are some throw them out as we will already

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Unformatted text preview: rs and the factors of 2 are all the possible denominators. Here then is a list of all possible rational zeroes of this polynomial. ±1 = ±1 ±1 ±3 = ±3 ±1 ±9 = ±9 ±1 ±1 1 =± ±2 2 ±3 3 =± ±2 2 ±9 9 =± ±2 2 So, we’ve got a total of 12 possible rational zeroes, half are integers and half are fractions. [Return to Problems] The following fact will also be useful on occasion in finding the zeroes of a polynomial. Fact If P ( x ) is a polynomial and we know that P ( a ) > 0 and P ( b ) < 0 then somewhere between a and b is a zero of P ( x ) . What this fact is telling us is that if we evaluate the polynomial at two points and one of the evaluations gives a positive value (i.e. the point is above the x-axis) and the other evaluation gives a negative value (i.e. the point is below the x-axis), then the only way to get from one point to the other is to go through the x-axis. Or, in other words, the polynomial must have a zero, since we know that zeroes are where a graph touches or crosses the x-axis. Note...
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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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