Lesson
Download
1 / 9

Video - PowerPoint PPT Presentation


  • 148 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Video' - mihaly


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
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
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:

    -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 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:

    -1 1 -2 1 -8 -12

    -1 3 -4 12

    1 -3 4 -12 0

    3 0 12

    1 0 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


ad