SOLUTION: How many positive zeros does f(x)= x^5-2x^4-3x^3+x^2+x-1 have?

Question 1158937: How many positive zeros does f(x)= x^5-2x^4-3x^3+x^2+x-1 have?
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

use Descartes' Rule of Signs

first sign: +
second sign: -
third sign: -
fourth sign:+
fifth sign:-
Then I count the number of changes:
from first sign to second sign:
from second sign to third sign:

from third to fourth sign:
from fourth to fifth sign:
There are sign changes in the positive-root case. This number "" is the maximum number of zeroes
so now I look at . That is, having changed the sign on, I'm now doing the negative-root case:
recall:,

from first sign to second sign:

from second sign to third sign:
from third to fourth sign:

from fourth to fifth sign:
There are sign changes in the negative-root case
so, since we have sign changes in the -root case, there will be positive root for sure

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