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6.6 Fundamental Theorem of Algebra

6.6 Fundamental Theorem of Algebra.

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6.6 Fundamental Theorem of Algebra

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  1. 6.6 Fundamental Theorem of Algebra 9.2.4.3 Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers, and from real numbers to complex numbers. In particular, non-real complex numbers are needed to solve some quadratic equations with real coefficients.

  2. Guiding Question: How can I write polynomials given zero’s and find zero’s of a polynomial? • Lesson Objective: I will be able to write a polynomial given roots and be able to find roots given a polynomial. • The following statements are equivalent. • A # (n) is a root of the polynomial P(x) • P(n) = 0 • n is an x-intercept of the graph P(n) • x – n is a factor of P(x) • When you divide P(x) by n, the remainder is 0 • n is a zero of P(x)

  3. Guiding Question: How can I write polynomials given zero’s and find zero’s of a polynomial? • Fundamental Thm. Of Algebra : Every polynomial function of degree n has at least 1 zero. • Every polynomial function of degree n has n zero’s, including multiplicities.

  4. Guiding Question: How can I write polynomials given zero’s and find zero’s of a polynomial? • Write the simplest Polynomial given a number of zero’s. 1. Zero’s are 1, 4, and -3 (Rewrite as binomial and multiply together) • What if there are irrational roots? Irrational Roots – have complex conjugates

  5. Guiding Question: How can I write polynomials given zero’s and find zero’s of a polynomial? Your turn, take 3 minutes Discuss with your table. 1. -2, 3, and 6 • 1, -2,

  6. Guiding Question: How can I write polynomials given zero’s and find zero’s of a polynomial? Given a polynomial, find the zero’s (roots) Find all the rational roots Graph the polynomial (find rational root) Test possible root Solve to find remaining roots.

  7. Guiding Question: How can I write polynomials given zero’s and find zero’s of a polynomial? Your turn, 5 minutes Discuss with your table when done. 1. 2.

  8. Guiding Question: How can I write polynomials given zero’s and find zero’s of a polynomial? • Assignment: Pg. 449 11-20 • Day 2 Pg. 449 24-29 • Day 3 Pg 449 30-36

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