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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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Video

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

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

Video

YouTube

sturmmath

Objective

Video

Example by Mrs. G

Give It a Try


Example by mrs g

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 g1

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 g2

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:

    -11-2 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 g3

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:

    -11-2 1 -8 -12

    -1 3 -4 12

    1-3 4 -12 0

    3 0 12

    10 4 0

3

reduced polynomial (quadratic)

Click to continue.

Objective

Video

Example by Mrs. G

Give It a Try


Example by mrs g4

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

Give It a Try

  • Find the number of zeros of the polynomial function.

  • Find all the zeros of the function.

Bring your work and answer to our next class!

Objective

Video

Example by Mrs. G

Give It a Try


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