Solving Polynomials 2017.notebook October 26, 2017
Warm‐Up1. A rectangular painting has dimensions x and x + 10. The painting is in a frame 2 in. wide. The total area of the picture and the frame is 900 in2. What are the dimensions of the painting?
2. Your community wants to put a square fountain in a park. Around the fountain will be a sidewalk that is 3.5 ft wide. The total area that the fountain and sidewalk can be is 700ft2. What are the dimensions of the fountain?
3.
4.
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials 2017.notebook October 26, 2017
Fundamental Theorem of Algebra: Any polynomial of degree n ... has n roots
but we may need to use complex (imaginary) numbers
AND imaginary roots ALWAY come in pairs
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials‐ Find all possible solutions.
1. x4 + 2x3 ‐ 13x2 + 10x = 0
1. Degree:
2. Roots:
3. End Behavior: same direction/ up
4. Calculator y=(type equation)
5. Look at graph determine real/complex
6. 2nd Table, look for where y=0
x = 5,0,1,2
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials‐ Find all possible solutions.
2. 2x4 ‐ 5x3 ‐ 17x2 + 41x ‐21 = 01. Degree: 4
2. Roots: 4
3. End Behavior: same direction/ up (even degree)
4. Calculator y=(type equation)
5. Look at graph determine real/complex
6. 2nd Table, look for where y=0
7. Find complex roots by synthetic division.
x=3, 1
Solving Polynomials 2017.notebook October 26, 2017
WarmUp1)
Solving Polynomials 2017.notebook October 26, 2017
https://play.kahoot.it/#/k/58df2632fbcc472fbbff9f6446fceadd
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials‐ Find all possible solutions.
3. x3 ‐ 2x2 + 5x ‐ 10 = 0
1. Degree:
2. Roots:
3. End Behavior: (even/odd) ____________ direction(s)
4. Calculator y=(type equation)
5. Look at graph determine real/complex
6. 2nd Table, look for where y=0
7. Find complex roots by synthetic division.
__ real, __ complexx=
`
Solving Polynomials 2017.notebook October 26, 2017
1) When you finish, work on ALEKS HW
2) 187 Topics Due Friday!
Solving Polynomials 2017.notebook October 26, 2017
Solving Polynomials‐ Find all possible solutions.
4. x4 + x3 ‐ 7x2 ‐ 9x ‐ 18 = 0
1. Degree:
2. Roots:
3. End Behavior:
4. Calculator y=(type equation)
5. Look at graph determine real/complex
6. 2nd Table, look for where y=0
7. Find complex roots by synthetic division.
x=
__real, __complex
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