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Polynomial Advanced Properties - Upper and Lower Bounds - Exercise 3

Apply the Upper and Lower Bounds Theorem and synthetic division to find the smallest positive integer and the largest negative integer that are upper and lower bounds for the real zeros of f(x) = 6x3 - 4x2 + 3x - 2.  Also, what does the Intermediate Value Theorem say about the existence of a zero between the two x-values you checked?  OPTIONAL: Graph f(x) = 6x3 - 4x2 + 3x - 2  first on a graphing calculator to help in picking possible bounds. Note that the justification is already given - no further justification is needed.

 

STATEMENT JUSTIFICATION
f(x) = 6x3 - 4x2 + 3x - 2 Given
Upper and Lower Bounds Theorem
Division Algorithm (Synthetic Division)
Intermediate Value Theorem

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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