Question 1133831: Using Decarte’s theory list all possible rational solutions for the following equation.
F(x) = 14x^3-12x^2-7x+24
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! F(x) = 14x^3-12x^2-7x+24
2 changes of sign so either 2 or 0 positive zeros
F(-x)=-14x^3-12x^2+7x+24
1 change of sign so 1 possible negative zero
possibilities are
factors of 14: 1,2,7,14 (the denominator)
factors of 24: 1,2,3,4,6,8,12,24 (the numerator)
The possible rational roots are 1/1, 1/2, 1/7, 1/14
2/1, 2/2(1, already noted), 2/7, 2/14 (but that is 1/7 and has been used)
etc. not counting the rational roots twice.
There are 32 possibilities, but several appear twice.
There is 1 negative zero
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