The Fundamental Theorem of Algebra

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.

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

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

fx = (3x^2 – 4x -5)(2x^6 – 5)

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

a. 0 or 2

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

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, 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

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

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

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

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