3.6 Complex Zereos. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra says that...

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3.6 Complex Zereos

Transcript of 3.6 Complex Zereos. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra says that...

Page 1: 3.6 Complex Zereos. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra says that every polynomial with complex coefficients must have.

3.6 Complex Zereos

Page 2: 3.6 Complex Zereos. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra says that every polynomial with complex coefficients must have.

The Fundamental Theorem of Algebra

• The Fundamental Theorem of Algebra says that every polynomial with complex coefficients must have at least one complex zero.

• Remember real numbers like 7 can be considered complex when written as 7 + 0i. So any polynomial will have complex zeros.

• The degree of the polynomial tells you exactly how many complex roots exist

• Even degree polynomials may have no real roots while odd degree must have one real root.

• Remember, Imaginary roots exist in pairs.

Page 3: 3.6 Complex Zereos. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra says that every polynomial with complex coefficients must have.

The Complete Factorization Theorem

• The Complete Factorization Theorem states that for any polynomial with degree 1 or greater the polynomial can be written as P(x) = a(x – c1) (x – c2) (x – c3) .... (x – cn) where a and c1, c2, c3, ... cn are complex numbers.

• This means that a polynomial can be written in factored form.

Page 4: 3.6 Complex Zereos. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra says that every polynomial with complex coefficients must have.

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LESSON 14 – FUNDAMENTAL THEOREM of ALGEBRA PreCalculus - Santowski.

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2.5 The Fundamental Theorem of Algebra Students will use the fundamental theorem of algebra to determine the number of zeros of a polynomial. Students.

2.5 The Fundamental Theorem of Algebra Students will use the fundamental theorem of algebra to determine the number of zeros of a polynomial. Students.

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Holt McDougal Algebra 2 Fundamental Theorem of Algebra How do we use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation.

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Section 2.7 The Fundamental Theorem of Algebra

Section 2.7 The Fundamental Theorem of Algebra

1.6.11 The fundamental theorem of algebra

1.6.11 The fundamental theorem of algebra

2.12.1 Complex Zeros and the Fundamental Theorem of Algebra.

2.12.1 Complex Zeros and the Fundamental Theorem of Algebra.

Ye Olde Fundamental Theorem of Algebra - MAA Sectionssections.maa.org/mddcva/MeetingFiles/Spring2012Meeting/TalkSlides/Parson.pdfThe Fundamental Theorem of Algebra A non-constant polynomial

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The Weak Fundamental Theorem of Algebra

The Weak Fundamental Theorem of Algebra

EULER’S FORMULA AND THE FUNDAMENTAL THEOREM OF ALGEBRA

EULER’S FORMULA AND THE FUNDAMENTAL THEOREM OF ALGEBRA

Holt Algebra 2 6-6 Fundamental Theorem of Algebra 6-6 Fundamental Theorem of Algebra Holt Algebra 2 Use the Fundamental Theorem of Algebra and its corollary.

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Holt McDougal Algebra 2 3-6 Fundamental Theorem of Algebra Use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation of least.

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Theorem (Second Fundamental theorem of calculus)

Theorem (Second Fundamental theorem of calculus)

Section 2.4 The Fundamental Theorem of Algebra And Zeros of Polynomials.

Section 2.4 The Fundamental Theorem of Algebra And Zeros of Polynomials.

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Using the Fundamental Theorem of Algebra 6.7. Learning Targets Students should be able to… -Use fundamental theorem of algebra to determine the number.

Holt McDougal Algebra 2 6-6 Fundamental Theorem of Algebra Use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation of least.

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