Concept explainers
If the given statement is true or false.
Answer to Problem 157CR
The given statement is false.
Explanation of Solution
Given:
The statement: A fourth degree polynomial with real coefficients can have -5,
Concept Used:
Complex zeros: The complex zeros of a polynomial function with real coefficients always occur in the conjugate pairs.
A polynomial of degree n can have at most n zeros.
From the above theorem it is clear that, a fourth degree polynomial with real coefficients can have at most 4 zeros.
Now, suppose-5,
But as
Similarly,
But this implies that the given fourth degree polynomial has 6 zeros, which is not possible.
Hence, the assumption that-5,
Conclusion:
The given statement is false.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning