Trevor is studying a polynomial function f of x Three given roots of f of x are negative 7 , 2 i , and 7 Trevor concludes that f of x must be a polynomial with degree 3 Which statement is true?
Answer
A
Trevor is correct.
B
Trevor is not correct because negative 2 i must also be a root.
C
Trevor is not correct because there cannot be both rational and complex roots.
D
Trevor is not correct because there cannot be an odd number of roots.
Explanation
For a polynomial with real coefficients, any nonreal complex root must come with its complex conjugate. Since 2i is a root, −2i must also be a root. Together with the roots −7 and 7, that makes at least four roots, so the polynomial cannot be degree 3; Trevor is not correct.
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