Concept explainers
To calculate: The zeros of the function
Answer to Problem 34PPS
The 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
Observe that degree of polynomial is 3, so the functions has 3 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 is 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
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 2 and constant term is 28 Therefore, p is a factor of 28 and q is a factor of 2.
The possible combinations of
Next, construct a table with help of synthetic substitution to compute the value of
As observed two zeros are resulted at
Now, the depressed polynomial is obtained is
Factor the polynomial.
Either
That is,
Thus, the zeros of the function
Chapter 6 Solutions
Algebra 2
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