anonymous
  • anonymous
Solve for the inequality. x^3-3x^2<0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathstudent55
  • mathstudent55
First, you need to factor the left side.
anonymous
  • anonymous
x<3
mathstudent55
  • mathstudent55
@mathpanda123 Not so fast. Try x = 0

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anonymous
  • anonymous
I did. Right now I'm at \[x^2(x-3)<0\] I want to set \[x^2\] and (x-3) equal to zero and solve it that way
anonymous
  • anonymous
x<0 0
anonymous
  • anonymous
Does that work?
mathstudent55
  • mathstudent55
Set the factored polynomial equal to zero, and find the zeroes. Those are points of interest.
mathstudent55
  • mathstudent55
x^2(x - 3) = 0 x = 0, x = 0, x = 3 There are two different points of interest. x = 0 and x = 3
mathstudent55
  • mathstudent55
|dw:1371417614082:dw|
mathstudent55
  • mathstudent55
Now use a point from each region, and test it in the original equation.
anonymous
  • anonymous
Do I plug those numbers into the factored equation or the original?
mathstudent55
  • mathstudent55
Since -1 works, the region left of 0 works. |dw:1371417831518:dw|
mathstudent55
  • mathstudent55
Since 1 works, numbers between 0 and 3 work. |dw:1371417923573:dw|
mathstudent55
  • mathstudent55
The region to the right of 3 is not part of the solution. |dw:1371418066120:dw|
mathstudent55
  • mathstudent55
|dw:1371418182276:dw|
mathstudent55
  • mathstudent55
You can plug into the original inequality (like I did) or into the factored inequality.
anonymous
  • anonymous
Alright, that was really helpful. Thanks! :)
mathstudent55
  • mathstudent55
wlcm

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