Fundamental Theorem of Algebra

Slides:



Advertisements
Similar presentations
Notes 6.6 Fundamental Theorem of Algebra
Advertisements

SECTION 3.6 COMPLEX ZEROS; COMPLEX ZEROS; FUNDAMENTAL THEOREM OF ALGEBRA FUNDAMENTAL THEOREM OF ALGEBRA.
Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.
Section 5.6 – Complex Zeros; Fundamental Theorem of Algebra Complex Numbers Standard form of a complex number is: a + bi. Every complex polynomial function.
OBJECTIVES: 1. USE THE FUNDAMENTAL THEOREM OF ALGEBRA 2. FIND COMPLEX CONJUGATE ZEROS. 3. FIND THE NUMBER OF ZEROS OF A POLYNOMIAL. 4. GIVE THE COMPLETE.
The Fundamental Theorem of Algebra Section 4.6 beginning on page 198.
Sullivan Algebra and Trigonometry: Section 5.6 Complex Zeros; Fundamental Theorem of Algebra Objectives Utilize the Conjugate Pairs Theorem to Find the.
5.7 Apply the Fundamental Theorem of Algebra
Complex Zeros; Fundamental Theorem of Algebra
9.9 The Fundamental Theorem of Algebra
PRE-AP PRE- CALCULUS CHAPTER 2, SECTION 5 Complex Zeros and the fundamental Theorem of Algebra.
Rational Root and Complex Conjugates Theorem. Rational Root Theorem Used to find possible rational roots (solutions) to a polynomial Possible Roots :
Section 4.3 Zeros of Polynomials. Approximate the Zeros.
COMPLEX ZEROS: FUNDAMENTAL THEOREM OF ALGEBRA Why do we have to know imaginary numbers?
Section 3.3 Theorems about Zeros of Polynomial Functions.
Warm Up. Find all zeros. Graph.. TouchesThrough More on Rational Root Theorem.
Chapter 2 Polynomial and Rational Functions. Warm Up
THE FUNDAMENTAL THEOREM OF ALGEBRA. Descartes’ Rule of Signs If f(x) is a polynomial function with real coefficients, then *The number of positive real.
Essential Questions How do we use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation of least degree with given roots?
Complex Zeros and the Fundamental Theorem of Algebra.
3.6 Complex Zereos. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra says that every polynomial with complex coefficients must have.
Solving Polynomial Functions involving Complex Numbers.
7.5 Roots and Zeros Objectives: The student will be able to…
The Fundamental Theorem of Algebra It’s in Sec. 2.6a!!! Homework: p odd, all.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 5.6 Complex Zeros; Fundamental Theorem of Algebra.
1/27/ Fundamental Theorem of Algebra. Intro Find all zeros for each of the following: Multiplicity – When more than one zero occurs at the.
Section 4.6 Complex Zeros; Fundamental Theorem of Algebra.
2015/16 TI-Smartview 2.5 The Fundamental Theorem of Algebra.
Today in Pre-Calculus Notes: –Fundamental Theorem of Algebra –Complex Zeros Homework Go over quiz.
1 What you will learn today…  How to use the Fundamental Theorem of Algebra to determine the number of zeros of a polynomial function  How to use your.
The Fundamental Theorem of Algebra Intro - Chapter 4.6.
Objective: SWBAT understand and apply the Fundamental Theorem of Algebra and the Linear Factorization Theorem to find a polynomial given real and complex.
Warm-up Multiply the factors and write in standard form.
2.5 The Fundamental Theorem of Algebra. The Fundamental Theorem of Algebra The Fundamental Theorem of Algebra – If f(x) is a polynomial of degree n, where.
REMAINDER THEOREM HONORS ADVANCED ALGEBRA PRESENTATION 2-7.
Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA.
Every polynomial P(x) of degree n>0 has at least one zero in the complex number system. N Zeros Theorem Every polynomial P(x) of degree n>0 can be expressed.
Conjugate Pairs Theorem Every complex polynomial function of degree n  1 has exactly n complex zeros, some of which may repeat. 1) A polynomial function.
Section 4.1 Polynomial Functions and Models.
Section 2-6 Finding Complex Zeros. Section 2-6 Fundamental Theorem of Algebra Fundamental Theorem of Algebra Linear Factorization Theorem Linear Factorization.
Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.
“Is it better to be feared or respected? And I say, is it too much to ask for both?”
Fundamental Theorem of Algebra
Section 3.4 Zeros of Polynomial Functions
Notes Over 3.4 The Rational Zero Test
Algebra II Explorations Review ( )
Complex Zeros and the Fundamental Theorem of Algebra
Complex Zeros Objective: Students will be able to calculate and describe what complex zeros are.
The Fundamental Theorem of Algebra
Warm-up Multiply the factors and write in standard form.
Fundamental Theorem of Algebra
Rational Root and Complex Conjugates Theorem
3.8 Complex Zeros; Fundamental Theorem of Algebra
Section 3.4 Zeros of Polynomial Functions
If a polynomial q(x) is divided by x – 4, the quotient is 2
Lesson 2.5 The Fundamental Theorem of Algebra
Fundamental Theorem of Algebra
Zeros of a Polynomial Function
Apply the Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra
Fundamental Theorem of Algebra
Lesson: _____ Section 2.5 The Fundamental Theorem of Algebra
3.4 Zeros of Polynomial Functions: Real, Rational, and Complex
Fundamental Theorem of Algebra
6.7 Using the Fundamental Theorem of Algebra
1) Find f(g(x)) and g(f(x) to show that f(x) and g(x) are inverses
Pre-AP Pre-Calculus Chapter 2, Section 5
Fundamental Theorem of Algebra
Fundamental Theorem of Algebra
Presentation transcript:

Fundamental Theorem of Algebra Section 3.7 Complex Zeros; Fundamental Theorem of Algebra

OBJECTIVE 1

A polynomial of degree 5 whose coefficients are real numbers has the zeros -2, -3i, and 2+4i. Find the remaining two zeros.

OBJECTIVE 2

Find a polynomial f of degree 4 whose coefficients are real numbers and that has the zeros -2, 1, 4+i. Graph the polynomial. For leading coefficient of -1 5 -5 55 -55 For leading coefficient of 1 For leading coefficient of 2

OBJECTIVE 3

5 -5 25 -25 For leading coefficient of 1

5 -5 25 -25