Concept explainers
To calculate: The rational zeros of the function
Answer to Problem 6.8.9EP
The rational zeros 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
Rewrite it as,
Observe that degree of polynomial is 5, so the functions has 5 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
There are 3 sign changes, so there are 3 or 1 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
There is 1 negative real zero.
Next, construct a table with possible combinations of real and imaginary zeros.
Recall that the Rational zero theorem states that provided a polynomial
For the provided function leading coefficient is 1 and constant term is
The possible combinations of
Use the graphing utility to solve the equation
Therefore,
Thus, the rational zeros of the function
Chapter EP Solutions
Algebra 2
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