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Warm-up

Warm-up. Answers. Precalculus Lesson. 2.5. Check: Worksheet Complex Numbers Side 37 all Side 38 (x4). 2.5. Objective: Find all real and complex zeros of a polynomial function. Quiz Wednesday 2.4-2.5. Lesson. Powerpoint 2.5 Fundamental Theorem of Algebra

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Warm-up

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  1. Warm-up

  2. Answers

  3. PrecalculusLesson 2.5 Check: Worksheet Complex Numbers Side 37 all Side 38 (x4)

  4. 2.5 Objective: Find all real and complex zeros of a polynomial function. Quiz Wednesday 2.4-2.5

  5. Lesson Powerpoint 2.5 Fundamental Theorem of Algebra Notes hand-out 2.5

  6. Find all zeros of a polynomial function • All real and rational zeros show up as x-intercepts when graphed. • The rational zeros are in the list of possible rational zeros. P’s and Q’s! • The real zeros can be seen on the graph, but may not be in the list of “possibles”

  7. Fundamental Theorem of Algebra • The function will have the same number of zeros as the degree of the function, including all double roots and complex roots. • Complex roots do not show up as x-intercepts. • Complex roots occur as conjugate pairs. (I.e., if 3+2i is a zero of the function, then 3-2i must also be a zero of the function.

  8. Use the following methods to find all of the zeros. • Factor • Quadratic Formula or Completing the Square. • Rational Zeros Test (p/q) • Synthetic division or Long division • Factor from simpler form

  9. Special Factoring Patterns • x2-4 • X2+4 • X2-3 • X2+3

  10. Ex 1 find all the zeros of the function AND write the function as a product of linear factors. a)

  11. Find all the zeros b)

  12. Find all the zeros c)

  13. Ex 2 Use the given zero of f to find all of the zeros of f. Function zero of the function r=3i a)

  14. Zero of function b)

  15. Assignments Together: p. 177 # 45, 47 Classwork: p. 176 #13, 21, 33, 55, 63, 81 Homework(2.5) p. 176 #14, 28, 36, 40, 48, 56, 67, 80, 82, 84

  16. Closure How Many zeros will the function have?

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