3.6 Fundamental Theorem.notebook
September 21, 2016
Homework Questions
Bellwork
List all possible roots of the following equations
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For the second function: How did we denote that it was cubic?
This has to do with the fundamental theorem of algebra.
3.6 Lets put some FUN
damentals in math
We can use 0's to write equations of functions
Math Jargin
Every polynomial function of degree n≥1 has at least one zero, where a zero
may be a complex number.
Corollary: Every polynomial function of degree n≥1 has exactly n zeros,
including multiplicities
Given the 0's write a function: ­3, 1 and 1
2
What this means:
The degree of your polynomial dictates how many 0's you have
If you are a 5th degree with a zero of 6 then the multiplicity of that 0 is 6
Write a cubic function with the 0's: 3 and ­4
Ex. Write a quintic function with a zero at ­6 3
Write a polynomial with zeros at 0, ­7, and 4
and a power of 8
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Sep 15­5:00 PM
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3.6 Fundamental Theorem.notebook
September 21, 2016
Gotta make it complicated
You will only be dealing with polynomials with real coefficients. You may on the other hand have unreal or complex roots
Conjugates!
or the complex conjugate root theorem to be exact
If a +bi is a root then a­bi is also a root.
if √a is a root then ­√ a is a root
They can be radicals or imaginary numbers Because your original polynomial does not have imaginary numbers or radicals they must be balanced out....... How?
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What about radicals?
They have conjugates too
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Now lets find our imaginary roots
We cannot leave unfactored pieces the final answer will have to be the product of linear factors
Write a polynomial with the following roots
1+i, √ 2, and ­3
Write a polynomial with roots at 2i, 1+√ 2 and 3 Find all roots of x4+4x3­x2+16x­20=0 Sep 15­5:20 PM
Sep 15­5:27 PM
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3.6 Fundamental Theorem.notebook
September 21, 2016
Homework Page 193 11­23 all 24­34 even Sep 15­5:37 PM
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