chapter 11 polynomial functions
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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
Chapter 11 Polynomial Functions
11.1 and 11.2Finding real roots of polynomials and the Fundamental Theorem of Algebra
Sounds impressive right?!
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!!
graphs
X = 0, 3, -4
X = 2,
X = -5, 2i, -2i
Let’s go to the real world!
Oops! Wrong real world!
How about the real number world??
Solve each poly by factoring
Multiplicity…look we’re identical!
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)
Rational Root Theorem
Joke Break!
• Why is the rational root problem so polite?
• It minds it’s p’s and q’s!
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
AssignmentPg. 342 (15-22 all)