Lesson Check Worksheet Complex Numbers Side 37 all Side 38 x4 25 Objective Find all real and complex zeros of a polynomial function ID: 803205
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Slide1
Warm-up
Slide2Answers
Slide3Precalculus
Lesson
Check:
Worksheet Complex Numbers
Side 37 all Side 38 (x4)
2.5
Slide4Objective: Find all real and complex zeros of a polynomial function.
2.5
Quiz Wednesday
2.4-2.5
Slide5Lesson
Powerpoint 2.5 Fundamental Theorem of Algebra
Notes hand-out 2.5
Slide6Find
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”
Slide7Fundamental 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.
Slide8Use 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
Slide9Special Factoring Patterns
x
2
-4
X
2+4X2-3
X2+3
Slide10Ex 1
find all the zeros of the function AND write the function as a product of linear factors.
a)
Slide11Find all the zeros
b)
Slide12Find all the zeros
c)
Slide13Ex 2
Use the given zero of
f
to find all of the zeros of
f
.Function zero of the function a)
r=3i
Slide14Zero of function
b)
Slide15Together:
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, 84Assignments
Slide16Closure
How Many zeros will the function have?