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What is the number of possible positive zeros and number of possible negative zeros of this polynomial function: \(f(x)=x^4+2x^3−11x^2−5x−6\) 

 Jan 16, 2020
 #1
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+5

The graph should help:

 

 Jan 16, 2020
 #2
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+1

The coefficient signs run + + - - -, just one change, so Descartes' rule of signs says that there is precisely one positive root.

Replace x by - x to get

 \(\displaystyle f (-x)=x^{4}-2x^{3}-11x^{2}+5x-6,\)

and you see three sign changes, indicating three or one negative roots. 

 Jan 16, 2020

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