SOLUTION: Please help w/ the following: Using Descartes Rule of Signs to determine how many positive and how many negative real zeros the polynomial functions may have. Do not attempt to

Algebra ->  Systems-of-equations -> SOLUTION: Please help w/ the following: Using Descartes Rule of Signs to determine how many positive and how many negative real zeros the polynomial functions may have. Do not attempt to      Log On


   

Question 62519: Please help w/ the following:
Using Descartes Rule of Signs to determine how many positive and how many negative real zeros the polynomial functions may have. Do not attempt to find the zeros.

f(x)=x^6-4x^5-x^4-3x^3+3x^2+x+4
Thank You.

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Please help w/ the following:
Using Descartes Rule of Signs to determine how many positive and how many negative real zeros the polynomial functions may have. Do not attempt to find the zeros.
f(x)=x^6-4x^5-x^4-3x^3+3x^2+x+4
Thank You.
TO FIND NUMBER OF POSSIBLE POSITIVE ROOTS..
1.WRITE F(X) IN DESCENDING ORDER..
IT IS ALREADY WRITTEN HERE.
2.FIND NUMBER OF CHANGES IN SIGNS OF COEFFICIENTS OF TERMS OF F(X)..
THERE ARE 2 CHANGES ...+1X^6 TO -4X^5...AND...-3X^3 TO +3X^2.
HENCE THERE WILL BE A MAXIMUM OF 2 POSITIVE ROOTS.
NEXT TO FIND THE NUMBER OF POSSIBLE NEGATIVE ROOTS..
1.WRITE F(-X) IN DESCENDING ORDER..
IT IS ...
F(-X)= X^6+4X^5-X^4+3X^3+3X^2-X+4
2.FIND NUMBER OF CHANGES IN SIGNS OF COEFFICIENTS OF TERMS OF F(-X)..
THERE ARE 3 CHANGES ...+4X^5 TO -X^4...AND...-X^4 TO +3X^3....AND
+3X^2 TO -X
HENCE THERE WILL BE A MAXIMUM OF 3 NEGATIVE ROOTS.