
Concept explainers
To find: the possible number of positive, negative, imaginary real zeroes of the given function.

Answer to Problem 21PT
The table for the possible combination of real and imaginary zeroes is:
Positive real zeroes | Negative Real zeroes | Imaginary real zeroes | Total zeroes |
Explanation of Solution
Given:
Concept used:
Descartes rule of sign:
Look at the change in the sign of the positive to negative or negative to positive.
The number of positive real zeroesis either equal to number of sign change of
For negative real zeroes the
Look at the change in the sign of the positive to negative or negative to positive.
The number of negative real zeroes is either equal to number of sign change of
Sum Positive real zeroes, negative real zeroes and imaginary zeroes equals to the total zeroes of the polynomial through this the imaginary zeroes can be calculated.
Calculation:
According to the given the polynomial equation is:
The total zeroes here is
Solving through Descartes rule of sign as:
The number of positive real zeroes is either equal to number of sign change of
Similarly,
The number of negative real zeroes is either equal to number of sign change of
There is one sign change in
There is two sign change in
Hence, the table for the possible combination of real and imaginary zeroes is:
Positive real zeroes | Negative Real zeroes | Imaginary real zeroes | Total zeroes |
Chapter 6 Solutions
Algebra 2
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