The Fundamental Theorem of Algebra

If f(x) is a third degree polynomial function, how many distinct complex roots are possible?

a. 0 or 2

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

How many x intercepts appear on the graph of this polynomial function? f(x)= x^4 - x^3 + x^2 - x

b. 2 x intercepts

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

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).

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

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.

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

Which of the following describes the roots of the polynomial function f(x) = (x - 3)^4 (x + 6)^2?

d. 3 with multiplicity 4 and -6 with multiplicity 2

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 4x^5 - 3x

d. 5 roots

Patricia is studying a polynomial function f(x). Three given roots of f(x) are -11-√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+√2i must be roots.

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 6 roots?

d. f(x) = 7x^6 + 3x^3 + 12

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?

fx = (3x^2 - 4x -5)(2x^6 - 5)