Lesson 3: The Fundamental Theorem of Algebra

Question 1

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

Question 2

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?

Revolt · Accepted Answer

Trevor is not correct because –2i must also be a root.

Question 3

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 4

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 5

If f(x) is a third degree polynomial function, how many distinct imaginary roots are possible?

Revolt · Accepted Answer

0 or 2

Question 6

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 7

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

Revolt · Accepted Answer

7 roots

Lesson 3: The Fundamental Theorem of Algebra Answers

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