chapter 11 polynomial functions
DESCRIPTION
11.1 and 11.2 Finding real roots of polynomials and the Fundamental Theorem of Algebra Sounds impressive right?!. Chapter 11 Polynomial Functions. Fundamental Theorem of Algebra. Every polynomial with degree n has “n” number of roots (zeros, x-intercepts, solutions!) - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/1.jpg)
Chapter 11 Polynomial Functions
11.1 and 11.2Finding real roots of polynomials and the Fundamental Theorem of Algebra
Sounds impressive right?!
![Page 2: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/2.jpg)
Fundamental Theorem of Algebra
• Every polynomial with degree n has “n” number of roots (zeros, x-intercepts, solutions!)
• These can be real (rational and irrational), complex (imaginary), or a combination of both! FUN!!
![Page 3: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/3.jpg)
graphs
X = 0, 3, -4
X = 2,
X = -5, 2i, -2i
![Page 4: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/4.jpg)
Let’s go to the real world!
Oops! Wrong real world!
How about the real number world??
![Page 5: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/5.jpg)
Solve each poly by factoring
![Page 6: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/6.jpg)
Multiplicity…look we’re identical!
![Page 7: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/7.jpg)
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ID the roots and state multiplicity
𝑥3+6 𝑥2+12 𝑥+8=0
𝑥4+8 𝑥3+18 𝑥2−27=0
(x + 2)(x + 2)(x + 2)
(x + 3)(x + 3)(x + 3)(x – 1)
![Page 9: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/9.jpg)
Rational Root Theorem
![Page 10: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/10.jpg)
Joke Break!
• Why is the rational root problem so polite?
• It minds it’s p’s and q’s!
![Page 11: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/11.jpg)
Find the roots
𝑥3+3 𝑥2−10 𝑥−24=0• Doesn’t factor• Use rational root theorem to ID
possible roots• Use synthetic to test for root
(remainder of zero)• Knock down to factorable poly
(usually quadratic)• Factor for the other roots• List the roots
![Page 12: Chapter 11 Polynomial Functions](https://reader033.vdocuments.mx/reader033/viewer/2022061617/5681613e550346895dd0a5a3/html5/thumbnails/12.jpg)
AssignmentPg. 342 (15-22 all)