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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Try factoring.

x%5E4-x%5E3-12x%5E2%3E=0

x%5E2%28x%5E2-x-12%29%3E=0

x%5E2%28x-4%29%28x%2B3%29%3E=0

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:
highlight_green%28x%3C-3%29
highlight_green%28-3%3Cx%3C0%29
highlight_green%280%3Cx%3C4%29
highlight_green%284%3Cx%29
Be sure you do that.

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

graph%28300%2C300%2C-5%2C5%2C-12%2C12%2Cx%5E4-x%5E3-12x%5E2%29

The summary answer of what you should understand from all this is that the solution is the set of points:
x%3C=-3 and x=0 and x%3E=4,
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.