the fundamental theorem of algebra l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
The Fundamental Theorem of Algebra PowerPoint Presentation
Download Presentation
The Fundamental Theorem of Algebra

Loading in 2 Seconds...

play fullscreen
1 / 8

The Fundamental Theorem of Algebra - PowerPoint PPT Presentation


  • 309 Views
  • Uploaded on

The Fundamental Theorem of Algebra. Lesson 4.5. Example. Consider the solution to Note the graph No intersections with x-axis Using the solve and csolve functions. Fundamental Theorem of Algebra. A polynomial f(x) of degree n ≥ 1 has at least one complex zero

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 'The Fundamental Theorem of Algebra' - jana


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
example
Example
  • Consider the solution to
  • Note the graph
    • No intersectionswith x-axis
  • Using the solve andcsolvefunctions
fundamental theorem of algebra
Fundamental Theorem of Algebra
  • A polynomial f(x) of degree n ≥ 1 has at least one complex zero
    • Remember that complex includes reals
  • Number of Zeros theorem
    • A polynomial of degree n has at most n distinct zeros
  • Explain how theorems apply to these graphs
constructing a polynomial with prescribed zeros
Constructing a Polynomial with Prescribed Zeros
  • Given polynomial f(x)
    • Degree = 4
    • Leading coefficient 2
    • Zeros -3, 5, i, -i
  • Determine factored form
  • Determine expanded form
conjugate zeroes theorem
Conjugate Zeroes Theorem
  • Given a polynomial with real coefficients
  • If a + biis a zero, then a – bi will also be a zero
finding imaginary zeros
Finding Imaginary Zeros
  • Given
  • Determine all zeros
    • Use calculator to factor
      • Try cFactor command
    • Use calculator to graph
    • Use cSolve or cZeros
application
Application
  • Complex numbers show up in study of electrical circuits
    • Impedance, Z
    • Voltage, V Can be represented by
    • Current, I complex numbers
  • Find missing value
assignment
Assignment
  • Lesson 4.5
  • Page 307
  • Exercises 1 – 41 EOO 43 – 47 odd