The Fundamental Theorem of Algebra

Question 1

crossesdoes not intersect✔ touches

Revolt · Accepted Answer

✔ touches

Question 2

✔ crossesdoes not intersecttouches

Revolt · Accepted Answer

✔ crosses

Question 3

g(x) = (x + 4)4(x − 9)

Revolt · Accepted Answer

✔ touches; At x = −4, the graph the x–axis.: touches; At x = 9, the graph the x–axis.: crosses

Question 4

✔ crossesdoes not intersecttouches

Revolt · Accepted Answer

✔ crosses

Question 5

If you know a root of a function is , then _____.

Revolt · Accepted Answer

is a known root.

Question 6

f (x) has two real roots and one imaginary root.f (x) has three real roots.f (x) has five real roots.f (x) has three real roots and two imaginary roots.

Revolt · Accepted Answer

f (x) has three real roots and two imaginary roots.

Question 7

Identify all of the root(s) of g(x) = (x2 + 3x - 4)(x2 - 4x + 29).

Revolt · Accepted Answer

1; -4; 2 + 5i; 2 - 5i

Question 8

Use the fundamental theorem of algebra and the complex conjugate theorem to determine the number and nature of the remaining root(s). Explain your thinking.

Revolt · Accepted Answer

The polynomial is degree 3, so it has three roots counting multiplicity. Two roots are given, leaving one remaining root. If the given roots are non-real complex conjugates, the remaining root must be real, since non-real roots occur in conjugate pairs.

Question 9

Did you include the following in your response?

Revolt · Accepted Answer

The degree of the polynomial is 3.; By the fundamental theorem of algebra, the function has three roots.; Two roots are given, so there must be one root remaining.; By the complex conjugate theorem, imaginary roots come in pairs.

The Fundamental Theorem of Algebra Answers

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