Concept explainers
To find: all real zeros of the function.
The only real zeros are
Given information:
The function
Formula used:
The Rational Zero Theorem:
If
Calculation:
Consider the function
Then
Since the leading coefficient is
Test these potential zeros by the synthetic division until we have found a zero. If a test number is a zero, the last number of the last row of the synthetic division will be
Here, since all the coefficients are positive, testing any positive number will not work (i.e., it won't be a zero). So, test the negative numbers, and the first one should always be
Let's test
\polyhornerscheme
And
Now, use the last row (without the last number
Let's test
L polyhorner scheme
And
Using synthetic division, the polynomial has a degree of
By using the last row of the synthetic division, we have
However, this is not factorable so, use the quadratic formula:
However, these two zeros are imaginary.
Therefore, the only real zeros are
Chapter 2 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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