AnswersAlgebra II A-ICThe Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra Answers

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

A
f (x) = (3 x squared minus 4 x minus 5) (2 x Superscript 6 Baseline minus 5)
Option A
B
f (x) = (3 x Superscript 4 Baseline + 2 x) Superscript 4
Option B
C
f (x) = (4 x squared minus 7) cubed
Option C
D
f (x) = (6 x Superscript 8 Baseline minus 4 x Superscript 5 minus 1) (3 x squared minus 4)
Option D
2
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How many x-intercepts appear on the graph of this polynomial function?

Question illustration
A
1 x-intercept
B
2 x-intercepts
C
3 x-intercepts
D
4 x-intercepts
3

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

A
0 or 2
B
0, 1, 2, or 3
C
1 or 2
D
1, 2, or 3
4

Patricia is studying a polynomial function f(x). Three given roots of f(x) are , 3 + 4i, and 10. Patricia concludes that f(x) must be a polynomial with degree 4. Which statement is true?

Question illustration
A
Patricia is correct because must be a root.
Option A
B
Patricia is correct because 3 – 4i must be a root.
C
Patricia is not correct because both 3 – 4i and must be roots.
Option C
D
Patricia is not correct because both 3 – 4i and must be roots.
Option D
5

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?

A
f (x) = (x minus 1) (x + 1) Superscript 11
Option A
B
f (x) = (x + 2) cubed (x squared minus 7 x + 3) Superscript 4
Option B
C
f (x) = (x Superscript 5 Baseline + 7 x + 14) Superscript 6
Option C
D
f (x) = 11 x Superscript 5 Baseline + 5 x + 25
Option D
6

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
B
Negative one-ninth i
Option B
C
One-ninth i
Option C
D
9 – i
7

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?

A
f(x) has three imaginary roots.
B
f(x) has three real roots.
C
f(x) has two real roots and two imaginary roots.
D
f(x) has three real roots and one imaginary root.
8

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?f(x) = 4x5 – 3x

A
1 root
B
2 roots
C
4 roots
D
5 roots
9

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?(9x + 7)(4x + 1)(3x + 4) = 0

A
1 root
B
3 roots
C
4 roots
D
9 roots
10

How many x-intercepts appear on the graph of this polynomial function?

Question illustration
A
1 x-intercept
B
2 x-intercepts
C
3 x-intercepts
D
4 x-intercepts

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