The Fundamental Theorem of Algebra

Question 1

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?

Revolt · Accepted Answer

Patricia is not correct because both 3 – 4i and must be roots.

Question 2

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

Revolt · Accepted Answer

If 1 + 13i is a root of f(x), then 1 – 13i is also a root of f(x).

Question 3

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?

Revolt · Accepted Answer

f(x) has three real roots.

Question 4

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

Revolt · Accepted Answer

5 roots

Question 5

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

Revolt · Accepted Answer

–3 – i

Question 6

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

Revolt · Accepted Answer

3 with multiplicity 4 and –6 with multiplicity 2

Question 7

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

Revolt · Accepted Answer

f (x) = (3 x squared minus 4 x minus 5) (2 x Superscript 6 Baseline minus 5)

Question 8

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

Revolt · Accepted Answer

3 roots

Question 9

If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?

Revolt · Accepted Answer

–9i

Question 10

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

Revolt · Accepted Answer

f (x) = 7 x Superscript 6 Baseline + 3 x cubed + 12

The Fundamental Theorem of Algebra Answers

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