
Concept explainers
(a)
The maximum number of real zeros of the function
(a)

Answer to Problem 2CT
Solution:
The maximum number of real zeros of
Explanation of Solution
Given information:
The function,
Let, the function
The maximum number of real zeros is the degree of the polynomial.
Here, the degree of
Therefore, the maximum number of real zeros of
(b)
The list of potential rational zeros of the function
(b)

Answer to Problem 2CT
Solution:
The list of potential zeros of
Explanation of Solution
Given information:
The function,
Let, the function
Now, to list the potential rational zeros of
By rational root theorem,
The divisors of the constant term are
The divisors of the leading coefficient are
Then, possible rational zeros of the polynomial are,
Therefore, the list of potential zeros of
(c)
The real zeros of
(c)

Answer to Problem 2CT
Solution:
The real zeros of
Explanation of Solution
Given information:
The function,
Let, the function
From part (b),
The potential rational zeros of
Now, test
Here, since the remainder is
After taking
Then, the depressed equation is,
By quadratic formula;
The factors of
The factor form of
Hence, the real zeros of
(d)
The
(d)

Answer to Problem 2CT
Solution:
The
Explanation of Solution
Given information:
The function,
To find
Thus the
Now to find
Hence the
(e)
Whether the graph crosses or touches the
(e)

Answer to Problem 2CT
Solution:
The graph crosses the
Explanation of Solution
Given information:
The function,
From part (c) the factors of the function
The graph of the function
(f)
The power function that the graph of
(f)

Answer to Problem 2CT
Solution:
The graph of the function
Explanation of Solution
Given information:
The function,
The polynomial function is
Here the degree of the polynomial function
The graph of the function
(g)
To graph: The function,
(g)

Explanation of Solution
Given information:
The function,
Graph:
The polynomial function is
From all the above parts, the analysis of the function
The graph of the function
The zeros of the function are
The
The graph crosses the
Here the degree of the polynomial function
Using all these information, the graph will look alike:
Now find additional points on the graph on each side of
For
For
For
For
For
Now plot all these coordinates
So the graph of the function is as follows,
Interpretation:
The graph of the function
The
The graph crosses the
Here the degree of the polynomial function
Chapter 4 Solutions
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