Question 428597: Use the Rational Root Theorem to list all possible rational roots of the polynomial equation.
x^3+x^2-7x-4=0
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the rational roots theorem helps you list all possible solutions to the quadratic equation.
a good reference for the rational roots test is at the following link.
http://www.purplemath.com/modules/rtnlroot.htm
using concepts discussed in this tutorial, your problem would be analyzed as follows:
your equation is;
x^3+x^2-7x-4=0
the constant term is -4 which has factors of +/- {1,2,4}
the coefficient of the leading term is 1 which yields +/- {1}
your possible factors are:
+/- {1,2,4} / {1} which yields +/- {1,2,4}
if we graph your equation, we can see where the possible roots lie.
a graph of your equation is shown below:
it doesn't not appear that any of the potential roots will solve this equation as it doesn't appear that they are rational, or, if rational, certainly not part of the potential roots given by the rational root theorem.
that happens.
these are only potential roots.
some of them could be the actual roots, but not necessarily.
read the reference.
it contains nice explanations as to what happens and how to extract the potential roots using the rational root theorem.
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