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  • Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester
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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

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Page 1: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 2: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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 

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 3: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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.

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 4: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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  = ___  

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 5: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 6: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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?

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 7: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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  = __  

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 8: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 9: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 10: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 11: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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:

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 12: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 13: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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:

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 14: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm
Page 15: Solving Polynomial Equations - BattalySolving Polynomial Equations ©2013, G. Battaly 2 May 06, 2013 Jan 2312:50 PM College Algebra Home Page Class Notes: Prof. G. Battaly, Westchester

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

http://www.battaly.com/collegealgebra
http://www.battaly.com/collegealgebra/homework/6_6_solving_polynomials.htm

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