SOLUTION: hello! how are you?could u please help me with this i have similar question on my test tonite ,thank you: Show that a=-3 and b =1 are the lower and upper bounds fro all zeros of t

Question 131517: hello! how are you?could u please help me with this i have similar question on my test tonite ,thank you:
Show that a=-3 and b =1 are the lower and upper bounds fro all zeros of the polynomial

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Show that a=-3 and b =1 are the lower and upper bounds fro all zeros of the polynomial
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There are several ways to do this.
One is to find all the zeroes.
----------
Use synthetic division:
-2)....2....5.....1....-2
........2....1....-1..|..0
so x=-2 is a zero
Since the quotient is 2x^2+x-1
There are two other zeros:
x = [-1 +- sqrt(1-4*2*-1))/4
x = [-1 +- sqrt(9)]/4
x = 1/2 or x = -1
-----------------------
So x=-3 and x=1 are definately lower and upper bounds
=============
Cheers,
Stan H.
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