Find a Polynomial of Least Degree with Only Real Coefficients $$2 + i , 4$$

question 166

Multiple Choice

Find a polynomial of least degree with only real coefficients and having the given zeros.
- $$2 + i , 4$$

• A) \(f ( x ) = x ^ { 3 } + 8 x ^ { 2 } + 21 x + 20\)
• B) \(f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 20 x + 20\)
• C) \(f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 21 x - 20\)
• D) \(f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - ( 3 - 4 i ) x + 12 + 16 i\)

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Definitions:

Greater Frequency

Refers to the higher rate of occurrence or action, commonly used in the context of events or processes happening more often.

Homologous Structures

Anatomical features in different species that arise from a common ancestor, showing evolutionary relationships despite their possible different functions.

Evolutionary Relationship

The connection and lineage between species or groups of organisms based on their shared genetic heritage and evolutionary history.

Homoplasy

The occurrence of similar traits in species due to convergent evolution or parallel evolution, not shared ancestry.