Answers GA-Advanced Algebra Concepts and ConnectionsThe Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra Answers

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

–3 with multiplicity 2 and 6 with multiplicity 4

–3 with multiplicity 4 and 6 with multiplicity 2

3 with multiplicity 2 and –6 with multiplicity 4

3 with multiplicity 4 and –6 with multiplicity 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)?

–3 – i

–3i

3 – i

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?

Patricia is correct because must be a root.

Patricia is correct because 3 – 4i must be a root.

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

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

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

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

f (x) = (3 x Superscript 4 Baseline + 2 x) Superscript 4

f (x) = (4 x squared minus 7) cubed

f (x) = (6 x Superscript 8 Baseline minus 4 x Superscript 5 minus 1) (3 x squared minus 4)

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

1 x-intercept

2 x-intercepts

3 x-intercepts

4 x-intercepts

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

1 root

3 roots

4 roots

9 roots

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?

Trevor is correct.

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

Trevor is not correct there cannot be an odd number of roots.

Trevor is not correct because there cannot be both rational and complex roots.