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The Fundamental Theorem of Algebra Answers

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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
2
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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
3

Which of the following describes the roots of the polynomial function ?

Question illustration
A
–3 with multiplicity 2 and 6 with multiplicity 4
B
–3 with multiplicity 4 and 6 with multiplicity 2
C
3 with multiplicity 2 and –6 with multiplicity 4
D
3 with multiplicity 4 and –6 with multiplicity 2
4

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
5

Trevor is studying a polynomial function f(x). Three given roots of f(x) are –7, 2i, and 7. Trevor concludes that f(x) must be a polynomial with degree 3. Which statement is true?

A
Trevor is correct.
B
Trevor is not correct because –2i must also be a root.
C
Trevor is not correct there cannot be an odd number of roots.
D
Trevor is not correct because there cannot be both rational and complex roots.
6

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
7

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
8

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
9

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
10

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

A
f (x) = 5 x Superscript 4 Baseline + 10 x squared + 2
Option A
B
f (x) = 5 x Superscript 5 Baseline + 3 x Superscript 4 Baseline + 12 x cubed + 7 x squared minus 2 x + 15
Option B
C
f (x) = 6 x Superscript 5 Baseline + x cubed minus 4 x squared + x minus 5
Option C
D
f (x) = 7 x Superscript 6 Baseline + 3 x cubed + 12
Option D

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