The Fundamental Theorem Of Algebra

7 September 2022
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13 test answers

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question
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?
answer
b. f(x) has three real roots.
question
If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?
answer
a. -9i
question
According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?
answer
fx = (3x^2 - 4x -5)(2x^6 - 5)
question
If f(x) is a third degree polynomial function, how many distinct complex roots are possible?
answer
a. 0 or 2
question
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 8x^7 - x^5 + x^3 + 6
answer
c. 7 roots
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Patricia is studying a polynomial function f(x). Three given roots of f(x) are -11-āˆš2i, 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true?
answer
d. Patricia is not correct because both 3 - 4i and -11+āˆš2i must be roots.
question
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? (9x + 7)(4x + 1)(3x + 4) = 0
answer
b. 3 roots
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Which of the following statements must be true about the polynomial function f(x)?
answer
b. If 1 + 13i is a root of f(x), then 1 - 13i is also a root of f(x).
question
According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?
answer
b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4
question
Which of the following describes the roots of the polynomial function f(x) = (x - 3)^4 (x + 6)^2?
answer
d. 3 with multiplicity 4 and -6 with multiplicity 2
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According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 4x^5 - 3x
answer
d. 5 roots
question
According to the Fundamental Theorem of Algebra, which polynomial function has exactly 6 roots?
answer
d. f(x) = 7x^6 + 3x^3 + 12
question
How many x intercepts appear on the graph of this polynomial function? f(x)= x^4 - x^3 + x^2 - x
answer
b. 2 x intercepts