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Example Question #1 : Solving Polynomial And Rational Inequalities
What is the solution to the following inequality?
First, we must solve for the roots of the cubic polynomial equation.
We obtain that the roots are .
Now there are four regions created by these numbers:
- . In this region, the values of the polynomial are negative (i.e.plug in and you obtain
- . In this region, the values of the polynomial are positive (when , polynomial evaluates to )
- . In this region the polynomial switches again to negative.
- . In this region the values of the polynomial are positive
Hence the two regions we want are and .
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