SOLUTION: How do you solve the following Polynomial Inequality? x^4 - x^3

SOLUTION: How do you solve the following Polynomial Inequality? x^4 - x^3 - 12x^2 greater than or equal to Zero

Question 919537: How do you solve the following Polynomial Inequality?
x^4 - x^3 - 12x^2 greater than or equal to Zero
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Try factoring.

The critical values are the roots: -3, 0, 4.
The values cut the x-axis into four intervals. The roots themselves are part of the solution set, because the inequality given is inclusive.

Test each of the intervals for truth or falsity:

Be sure you do that.

The graph for the function should be like this, just to help you check:

The summary answer of what you should understand from all this is that the solution is the set of points:
and and ,
that whole set of numbers are the possible solutions, but just not all at the same time. It's the SET that is the solution.
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