Concept explainers
To calculate: The number of positive real zeroes, negative real zeroes and imaginary zeroes of the function
Answer to Problem 6.7.8EP
The number of positive real zeroes, negative real zeroes and imaginary zeroes of the function
Explanation of Solution
Given information:
The function
Formula used:
A polynomial of n degree has n zeros, which can be either real or imaginary.
Descartes’ rule of signs states that consider a polynomial
Calculation:
Consider the function
Observe that degree of polynomial is 4, so the functions has 4 zeros which can be either real or imaginary.
Descartes’ rule of signs states that consider a polynomial
So, count the number of times the sign changes between the coefficients of
The coefficients are
There are 4 sign changes, so there are 4, 2 or 0 positive real zeros.
Now,
Descartes’ rule of signs states that consider a polynomial
So, count the number of times the sign changes between the coefficients of
The coefficients are
There is no sign change, so there are no negative real zeros.
Next, construct a table with possible combinations of real and imaginary zeros.
Chapter EP Solutions
Algebra 2
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