The Fundamental Theorem of Algebra Answers
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21
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Two roots of a third degree polynomial function f(x) are –4 and 4. Which statement describes the number and nature of all roots for this function?
A
f(x) has three imaginary roots.B
f(x) has three real roots.C
f(x) has two real roots and two imaginary roots.D
f(x) has three real roots and one imaginary root.22
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According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?f(x) = 4x5 – 3x
A
1 rootB
2 rootsC
4 rootsD
5 roots23
Patricia is studying a polynomial function f(x). Three given roots of f(x) are , 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true?
A
Patricia is correct because must be a root.
B
Patricia is correct because 3 – 4i must be a root.C
Patricia is not correct because both 3 – 4i and must be roots.
D
Patricia is not correct because both 3 – 4i and must be roots.
24
If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?
A
–9iB
Negative one-ninth i
C
One-ninth i
D
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