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Determine the set of all real x satisfying \(x^3-2x^2-3x<0.\) Enter your answer in interval notation.

waffles  Nov 14, 2017
edited by waffles  Nov 14, 2017
 #1
avatar+87604 
+3

x^3 -2x^2 - 3x < 0

 

Let's solve this

 

x^3 - 2x^2 - 3x  = 0      factor

 

x( x^2 - 2x - 3)  = 0

 

x( x - 3) ( x + 1)  = 0

 

Set   each factor to 0   and solve for x   and the solutions are

 

x = 0 , x = 3   and x = -1

 

We have four possible solution intervals

 

(-inf, -1), ( - 1, 0) , (0, 3)  and (3, inf )

 

This graph shows that the intervals in red are the correct solution intervals :

 

https://www.desmos.com/calculator/z8f6gksyuq

 

 

cool cool cool

CPhill  Nov 14, 2017

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