The Fundamental Theorem of Algebra

Question 1

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

Revolt · Accepted Answer

0 or 2

Question 2

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

Revolt · Accepted Answer

2 x-intercepts

Question 3

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 4

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 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?

Revolt · Accepted Answer

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

Question 6

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?

Revolt · Accepted Answer

f (x) = (x + 2) cubed (x squared minus 7 x + 3) Superscript 4

Question 7

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 8

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 9

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

Question 10

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)

The Fundamental Theorem of Algebra Answers

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