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

question

Patricia is studying a polynomial function f(x). Three given roots of f(x) are -11-ā2i, 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+ā2i 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

question

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

question

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