AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S1_2024The Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra Answers

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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
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

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
4

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
5

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
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

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.
8

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.
9

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
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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