The Fundamental Theorem of Algebra Answers

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1
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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
2
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How many x-intercepts appear on the graph of this polynomial function?

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

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
4

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
5

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.
6

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
7

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
8

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
9

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
10

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.

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