The Fundamental Theorem of Algebra Answers

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1
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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
2
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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
3

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?f(x) = 8x7 – x5 + x3 + 6

A
3 roots
B
4 roots
C
7 roots
D
8 roots
4

Which of the following statements must be true about the polynomial function f(x)?

A
If is a root of f(x), then is also a root of f(x).
Option A
B
If 1 + 13i is a root of f(x), then 1 – 13i is also a root of f(x).
C
If 13 is a root of f(x), then –13 is also a root of f(x).
D
If –13 + i is a root of f(x), then 13 + i is also a root of f(x).
5

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
6

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
7

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
8

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
9

If –3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

A
–3 – i
B
–3i
C
3 – i
D
3i
10

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

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