A26­5Notes.notebook
March 03, 2015
Algebra 2
Ch.6 Notes Page 33
P33 6­5 Theorems about Roots
of Polynomial Functions
Aug 19­6:20 AM
Rational Root Theorem
3
2
4x + 3x + 2x + 6
p
q
If p/q is in simplest form and is a rational root of a polynomial equation with integer coefficients, then p must be a factor of the constant and q must be a factor of the leading coefficient.
Oct 17­9:16 AM
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A26­5Notes.notebook
March 03, 2015
Feb 26­2:29 PM
Feb 26­2:32 PM
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A26­5Notes.notebook
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Roots
Feb 26­2:32 PM
Finding Rational Roots
x3 + x2 ­ 3x ­ 3 = 0
1. Find Factors of p (­3) +/­ 1 and +/­ 3
2. Find Factors of q (1) +/­ 1
3. List all possible factors p/q +/­ 1 and +/­ 3
4. Test each possible factor
to see if it works in the problem
Oct 27­7:22 AM
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A26­5Notes.notebook
March 03, 2015
Using the Rational Root Theorem
Find all of the roots (Rational or Complex)
Find the roots of the equation...
x3 ­ 2x2 ­ 5x + 10
1. List Possible Rational Roots first +/­ 1, +/­ 2, +/­ 5, +/­ 10
2. Test each Possible Rational Root +2 works
3. Use Synthetic Division with Root from Above
4. Find Remaining Roots
Oct 27­8:43 AM
Irrational Root Theorem
Conjugates
Number pairs of the form a + √b and a ­ √b
Irrational Root Theorem
If a + √b is a root of a polynomial equation with rational coefficients, then the conjugate a ­ √b also is a root.
A polynomial with rational coefficients has the roots 1 + √3 and ­√11
Find 2 additional Roots
Oct 27­8:56 AM
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A26­5Notes.notebook
March 03, 2015
Imaginary Root Theorem
Conjugates
Number pairs of the form a + bi and a ­ bi
Imaginary Root Theorem
If the imaginary number a + bi is a root of a polynomial equation with real coefficients, then the conjugate a ­ bi also is a root.
A polynomial with real coefficients has the roots 3 ­ i and 2i
Find 2 additional Roots
Oct 27­9:09 AM
HW #34
6­5 P339 #1,2,7,8,14,17,19,22
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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