IXL - Fundamental Theorem of Algebra (Algebra 2 practice)

Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.

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question

Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.

–

key idea

A number

is a root of a polynomial

(

)

(

)

The Fundamental Theorem of Algebra

(

)

is a polynomial of degree

≥

with complex coefficients, then

(

)

has at least one complex root.

Corollary to the Fundamental Theorem of Algebra

(

)

is a polynomial of degree

≥

with complex coefficients, then

(

)

has exactly

complex roots (including any repeated roots).

solution

First, find the degree of the polynomial.

–

The degree is 4. Since its coefficients are real, and all real numbers are also complex numbers, you can apply the Corollary to the Fundamental Theorem of Algebra.

So, including any repeated roots,

–

has 4 complex roots.

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