Upload
others
View
8
Download
0
Embed Size (px)
Citation preview
Solving Polynomial Equations
©2013, G. Battaly 1
May 06, 2013
Jan 2312:50 PM
6.6 Solving Polynomial Equations
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Study 6.6 # 17, 11, 15, 19, 27, 33, 47, 57, 6367, 97, 101
Homework
Solving Polynomial Equations
©2013, G. Battaly 2
May 06, 2013
Jan 2312:50 PM
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
6.6 Solving Polynomial Equations
x2 9 = 0 Solve:
Need to find the values of xthat make the statement true.
If a b = 0then either a = 0 or b = 0 or both
Multiplication Property of Zero: If a product = 0, then
at least one of the factors = 0
Solving Polynomial Equations
©2013, G. Battaly 3
May 06, 2013
Jan 2312:50 PM
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
6.6 Solving Polynomial Equations
x2 9 = 0 Solve:
If a b = 0then either a = 0 or b = 0 or both
Need a product. So, factor.
(x + 3)(x 3) = 0 a b = 0
x + 3 = 0 x 3 = 0 a = 0 b = 0
x = 3 x = 3
∴ x = 3 and x = 3 are both solutions.
Solving Polynomial Equations
©2013, G. Battaly 4
May 06, 2013
Jan 2312:50 PM
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
6.6 Solving Polynomial Equations
x2 6x + 9 = 0 Solve:
If a b = 0then either a = 0 or b = 0 or both
Need a product. So, factor.
( )( ) = 0 a b = 0
_____ = 0 ______ = 0 a = 0 b = 0
x = __ x = ___
Solving Polynomial Equations
©2013, G. Battaly 5
May 06, 2013
Jan 2312:50 PM
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
6.6 Solving Polynomial Equations
x2 6x + 9 = 0 Solve:
If a b = 0then either a = 0 or b = 0 or both
Need a product. So, factor.
(x 3)(x 3) = 0 a b = 0
x 3 = 0 x 3 = 0 a = 0 b = 0
x = 3 x = 3
∴ x = 3 is the solution
Solving Polynomial Equations
©2013, G. Battaly 6
May 06, 2013
Jan 2312:50 PM
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
6.6 Solving Polynomial Equations
x2 6x + 9 = 0 ∴ x = 3 is the solution
x2 9 = 0 ∴ solution: x = 3 and x = 3
f(x) = x2 9 f(x) = x2 6x + 9
How do our solutions relate to the graphsof the corresponding functions?
Solving Polynomial Equations
©2013, G. Battaly 7
May 06, 2013
Jan 2312:50 PM
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
6.6 Solving Polynomial Equations
x2 9 = 7 f(x) = x2 9
Not equal to 0. Need touse the APE so = 0 on right.
Solve:
x2 ___ = 0 (x +__)(x __) = 0
x +__ = 0 x __ = 0 x = __ x = __
Solving Polynomial Equations
©2013, G. Battaly 8
May 06, 2013
Jan 2312:50 PM
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
6.6 Solving Polynomial Equations
x2 9 = 7
∴ solution: x = 4 and x = 4
f(x) = x2 9
Not equal to 0. Need touse the APE so = 0 on right.
Solve:
x2 16 = 0 (x + 4)(x 4) = 0
x + 4 = 0 x 4 = 0 x = 4 x = 4
f(x) = x2 16
Solving Polynomial Equations
©2013, G. Battaly 9
May 06, 2013
May 14:27 PM
6.6 Solving Polynomial Equations
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
Solving Polynomial Equations
©2013, G. Battaly 10
May 06, 2013
May 14:29 PM
6.6 Solving Polynomial Equations
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
Solving Polynomial Equations
©2013, G. Battaly 11
May 06, 2013
May 14:29 PM
6.6 Solving Polynomial Equations
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
(x)2 = x2(4)2 = 16 and2(x)(4)=8x∴PerfectSq. Trinomial
Check:
Solving Polynomial Equations
©2013, G. Battaly 12
May 06, 2013
May 14:33 PM
6.6 Solving Polynomial Equations
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
Solving Polynomial Equations
©2013, G. Battaly 13
May 06, 2013
May 14:33 PM
6.6 Solving Polynomial Equations
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
Need: ax2 + bx + c = 0
Check:
Solving Polynomial Equations
©2013, G. Battaly 14
May 06, 2013
May 14:36 PM
6.6 Solving Polynomial Equations
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework
Solving Polynomial Equations
©2013, G. Battaly 15
May 06, 2013
May 14:36 PM
6.6 Solving Polynomial Equations
College Algebra Home Page
Class Notes: Prof. G. Battaly, Westchester Community College, NY
Homework