# The Fundamental Theorem Of Algebra

## Unlock all answers in this set

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?
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)?
a. -9i
question
According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?
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?
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
c. 7 roots
question
Patricia is studying a polynomial function f(x). Three given roots of f(x) are -11-ā2i, 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true?
d. Patricia is not correct because both 3 - 4i and -11+ā2i 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
b. 3 roots
question
Which of the following statements must be true about the polynomial function f(x)?
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?
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?