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Lesson. Video. 6.7. “What are we trying to accomplish?”. Algebra 2 2013-14. Example by Mrs. G. Give It a Try. Lesson 6.7. Use The Fundamental Theorem of Algebra to determine the number of zeros of a polynomial function. Find all zeros of a polynomial function. Objective. Video.

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Presentation Transcript

Lesson

Video

6.7

“What are we trying to accomplish?”

Algebra

2

2013-14

Example by Mrs. G

Give It a Try

Lesson 6.7
• Use The Fundamental Theorem of Algebra to determine the number of zeros of a polynomial function.
• Find all zeros of a polynomial function.

Objective

Video

Example by Mrs. G

Give It a Try

Video

sturmmath

Objective

Video

Example by Mrs. G

Give It a Try

Example by Mrs. G

GENERAL STATEMENT:

In general, when all real and imaginary solutions are counted

(with all repeated solutions counted individually), an nth-degree

polynomial has exactly n solutions. Similarly, an nth-degree

polynomial function has exactly n zeros.

Click to continue.

Objective

Video

Example by Mrs. G

Give It a Try

Example by Mrs. G

Ex 1: Finding the Number of Solutions/Zeros

• Equations have solutions, whereas functions have zeros, they are basically the same thing.
• How many zeros does the function have?
• Since it is a 4th degree function, there are 4 zeros.

Click to continue.

Objective

Video

Example by Mrs. G

Give It a Try

Example by Mrs. G
• Find all the zeros of
• Start by making a list of possible rational zeros:
• Test the rational zeros using synthetic division:

-1 1 -2 1 -8 -12

-1 3 -4 12

1 -3 4 -12 0

reduced polynomial (now cubic)

Click to continue.

Objective

Video

Example by Mrs. G

Give It a Try

Example by Mrs. G
• Find all the zeros of
• Continue to test the rational zeros using synthetic division and the reduced polynomial until your result is a quadratic:

-1 1 -2 1 -8 -12

-1 3 -4 12

1 -3 4 -12 0

3 0 12

1 0 4 0

3

Click to continue.

Objective

Video

Example by Mrs. G

Give It a Try

Example by Mrs. G
• Find all the zeros of
• Factored form:
• Set each factor = 0:
• Zeros:

Click to continue.

Objective

Video

Example by Mrs. G

Give It a Try

Give It a Try
• Find the number of zeros of the polynomial function.
• Find all the zeros of the function.