Question
Use the rational zeros theorem to list all possible zeros of the function
.
Enter the possible zeros separated by commas. You do not need to factor the polynomial.
Enter the possible zeros separated by commas. You do not need to factor the polynomial.
Ask by Bob Campbell. in the United States
Jan 31,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The possible rational zeros are: -3, -1, -3/5, -1/5, 1/5, 3/5, 1, 3.
Solution
The possible rational zeros of the function
can be determined using the Rational Zeros Theorem.
According to the theorem, any possible rational zero is of the form
, where:
-
is a factor of the constant term (which is 3). -
is a factor of the leading coefficient (which is 5).
Factors of 3 (constant term): ±1, ±3
Factors of 5 (leading coefficient): ±1, ±5
Factors of 5 (leading coefficient): ±1, ±5
Thus, the possible rational zeros are:
Listing them out:
Answer:
-3, -1, -3/5, -1/5, 1/5, 3/5, 1, 3
-3, -1, -3/5, -1/5, 1/5, 3/5, 1, 3
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Extra Insights
To apply the rational zeros theorem, we first need to identify the factors of the constant term (3) and the leading coefficient (5). The factors of 3 are ±1, ±3, and the factors of 5 are ±1, ±5.
Now, we can form all the possible combinations of these factors in the form of
, where
is a factor of 3 and
is a factor of 5. This results in the possible rational zeros:
±1, ±3, ±
, ±
So, the complete list of possible rational zeros is:
1, -1, 3, -3, , -
,
, -
1, -1, 3, -3,