A26­6Notes.notebook
March 04, 2015
Algebra 2
Ch.6 Notes Page 34
P34 6­6 The Fundamental Theorem of Algebra
Aug 19­6:20 AM
The Fundamental Theorem of Algebra
If P(x) is a polynomial of degree n > 1 with complex coefficients, (a + bi) then P(x) = 0 has at least one complex root.
Corollary to
The Fundamental Theorem of Algebra
Including complex roots and multiple roots, an nth degree polynomial equation has exactly n roots; the related polynomial function has exactly n zeros.
Oct 17­9:16 AM
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A26­6Notes.notebook
March 04, 2015
Using the Fundamental Theorem of Algebra
x3 + 2x2 ­ 4x ­ 6 = 0 Find the Number of Complex Roots
The possible Number of Real Roots
The possible Rational Roots
Based on Corollary to Fundamental Theorem (nth degree)
Based on Imaginary Root Theorem (Zero Imaginary or Two Imaginary)
Based on Rational Root Theorem (Possible Rational Roots are...)
Oct 27­9:43 AM
Practice
x4 ­ 3x3 + 4x + 1 = 0 Find the Number of Complex Roots
The possible Number of Real Roots
The possible Rational Roots
Oct 27­9:51 AM
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A26­6Notes.notebook
March 04, 2015
Finding All Zeros of a Polynomial Function
x3 + x2 ­ x + 2
Use Rational Root Theorem to Find a Rational Zero
(Get a remainder of Zero) Check +/­ 1 and +/­ 2 (­2 works)
Use Synthetic Division
Factor or Use Quadratic Equation
­2
1
1
­1
2
Oct 27­9:53 AM
HW #35
6­6 P343 #1­4,10,16
Please put your name and class period at the top of
the homework. Also include the homework number.
Aug 19­6:25 AM
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