Concept explainers
(a)
To find: The possible number of positive and negative real zeroes of the function
The possible number of positive zeores are 2 and negative real zeroes are 1.
Given information
Between the first two coefficients there are no change in signs but between second and third first change, then between our third and fourth second change .Descartes´ rule of signs tells that there are exactly 2 real positive zeros
In order to find the number of negative zeros we find f(-x) and count the number of changes in sign for the coefficients:
Here we can see that one changes of signs, hence there is one negative zeros
(b)
To find: The possible number of positive and negative real zeroes of the function
The positive roots are 0 and number of negative root is either 3 or 1.
Given information
There is no sign change between all the terms .hence there is no positive root.
In order to find the number of negative zeros we find f(-x) and count the number of changes in sign for the coefficients:
Here we can see that three changes of signs, hence there is 3 negative zeros or one negative zero
(c)
To find: The possible number of positive and negative real zeroes of the function
The positive roots are 1 and number of negative root is 0.
Given information
There is one sign change between all the terms .hence there is one positive root.
In order to find the number of negative zeros we find f(-x) and count the number of changes in sign for the coefficients:
Here we can see that there is no changes of signs, hence there is 0 negative zeros
(c)
To find: The possible number of positive and negative real zeroes of the function
The positive roots are 0 and number of negative root is 1.
Given information
There is one sign change between all the terms .hence there is one positive root.
In order to find the number of negative zeros we find f(-x) and count the number of changes in sign for the coefficients:
Here we can see that there is one change of signs, hence there is 1 negative zeros .
Chapter 2 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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