PRE-AP PRE- CALCULUS CHAPTER 2, SECTION 5 Complex Zeros and the fundamental Theorem of Algebra.

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PRE-AP PRE- CALCULUS CHAPTER 2, SECTION 5 Complex Zeros and the fundamental Theorem of Algebra

Use your device to answer the following questions…. What is an imaginary number? How do you represent an imaginary number? Why do we need imaginary numbers? What is a complex number?

Use your device…. Sketch an example of a graph that has no real zeros.

Theorem: Fundamental Theorem of Algebra A polynomial function of degree n has n complex zeros (real and nonreal). Some of these zeros may be repeated.

Something to understand…. Just because you can find a nonreal zero of a function doesn’t mean the graph touches or crosses the x-axis.

Write the polynomial in standard form, and identify the zeros of the function and the x- intercepts of the graph.

Theorem: Complex Conjugate Zeros

Complex conjugates ExpressionComplex conjugate

Finding a Polynomial from Given Zeros Write a polynomial function of minimum degree in standard form whose zeros include -3, 4, and 2 + i.

Finding a Polynomial from Given Zeros

Factoring a Polynomial with Complex Zeros

Finding Complex Zeros

Practice Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed. -1 (multiplicity 3), 3 (multiplicity 1)

Practice Find all of the zeros and write a linear factorization of the function

Find all the possible zeros of the function and determine which ones are the zeros. Factor completely.

Ch. 2.5 Homework Pg. 234 – 235, #’s: 3, 4, 8, 9, 14, 15, 27, 28, 38, 43, Total Problems Gray Book: