SOLUTION: topic: Descarte's rule of signs
use Descartes rule of signs to determine the possible numbers of positive and negative zeros of the following functions:
1) f(x)=5x^3+3x^2-6x+9
2
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Question 35214: topic: Descarte's rule of signs
use Descartes rule of signs to determine the possible numbers of positive and negative zeros of the following functions:
1) f(x)=5x^3+3x^2-6x+9
2) f(x)=-2x^5+4x^3-2x^2-5
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
use Descartes rule of signs to determine the possible numbers of positive and negative zeros of the following functions:
1) f(x)=5x^3+3x^2-6x+9..TO FIND MAXIMUM NUMBER OF POSITIVE ROOTS ,FIND THE NUMBER OF CHANGES IN COEFFICIENTS OF TERMS OF F(X)WRITTEN IN DECREASING ORDER.
THERE ARE 2 CHANGES IN SIGN OF COEFFICIENTS....(3X^2)3 TO -6(-6X) AND -6(-6X) TO 9(9)...HENCE MAXIMUM NUMBER OF POSITIVE ROOTS ARE 2
TO FIND MAXIMUM NUMBER OF NEGATIVE ROOTS ,FIND THE NUMBER OF CHANGES IN COEFFICIENTS OF TERMS OF F(-X)WRITTEN IN DECREASING ORDER.
F(-X)=-5X^3+3X^2+6X+9...
HERE WE HAVE ONLY ONE CHANGE IN SIGN OF COEFFICIENTS...FROM -5 (-5X^3)TO 3(3X^2)...HENCE MAXIMUM NUMBER OF NEGATIVE ROOTS ARE 1.
2) f(x)=-2x^5+4x^3-2x^2-5..I THINK YOU CAN DO THIS NOW ON THE ABOVE BASIS
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