Solve and Graph Polynomial Inequalities - Pre-Calculus
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Question
What is the solution to the following inequality?
What is the solution to the following inequality?
Answer
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 
.
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:
-
-
-
-
Hence the two regions we want are
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