Question 612074: Can you give me step by step how to solve..
List all of the possible rational zeros of
2x^4-5x^3+3x^2-12x-6
ALGEBRA 2 Problem.
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! The rational zeros theorem (also called the rational root theorem) is used to check whether a polynomial has rational roots (zeros). It provides a list of all possible rational roots of the polynomial equation , where all coefficients are integers. If the equation has rational roots p/q, where p and q are integers, then p must divide evenly into the constant term a0 and q must divide evenly into the leading coefficient an. In other words, p is a factor of ħa0 and q is a factor of ħan.
http://www.chegg.com/homework-help/definitions/rational-zeros-theorem-27
get all the factors in the high order coefficient. Then get all the factors in the constant term
2 -- -2,-1,1,2
-6 -- -6,-3,-2,-1,1,2,3,6
now make every combination of the ratio of factors of -6 to factors of 2
-6/-2, -6/-1, -6/1, -6/2, -3/-2, .... 6/-2, 6/-1, 6/1, 6/2
now eliminate all the duplicates, and you are done.
Note this does not mean all these numbers ARE roots, it merely says that if there are roots, then these are the only possible ones.
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