lesson 5.6 rational zeros of polynomial functions

LESSON 5.6 Rational Zeros of Polynomial Functions

Upload: julian-wilson

Post on 21-Jan-2016

242 views

Category:

Documents

0 download

Report

Download

Embed Size (px):

TRANSCRIPT

LESSON 5 .6

Rational Zeros of Polynomial Functions

Solve x3 – 5x2 + 8x – 4= 0. How? Can you factor this? Can you use the quadratic formula?

Now what if I tell you that one root is x =1?Then x3 – 5x2 + 8x – 4 = (x – 1)( ). Use synthetic division to find the missing factor.

The missing factor is x2 – 4x + 4, which can be factored. So solve and learn that x = 2.

So the solutions are 1 and 2 (double root).

Page 3: LESSON 5.6 Rational Zeros of Polynomial Functions

But what if you don’t know any zeros and cannot factor a polynomial?

Rational Zero TheoremTo find the possible rational zeros of a polynomial divide the factors of the constant by the factors of the leading coefficient.

List the possible rational zeros for f(x) = 2x3 + 3x2 – 4x + 6.

Answer: ±1,±2,±3,±6,±1/2,±3/2

Page 4: LESSON 5.6 Rational Zeros of Polynomial Functions

Now try this one….

a) Solve x3 + 4x2 + x – 6 = 0

Answer: x = 1, x = -2, x = -3

Do they all check?

Why do you think there were 3 solutions?

Page 5: LESSON 5.6 Rational Zeros of Polynomial Functions

and this one…

b) Find all of the roots of f(x) = x4 + 2x3 – 7x2 – 20x – 12

Answer: x = 3, -2 (double root) and -1. Verify this using your graphing calculator.

Page 6: LESSON 5.6 Rational Zeros of Polynomial Functions

and one last problem!

c) Find the zeros of f(x) = 6x4 – 25x3 + 30x2 – 5x – 6

How many answers should there be?Answer: x = 1, x = 2, x = 3/2, x = -1/3

2.4/2.52.4/2.5 Real Zeros of Polynomial Functions

Obj. 6 Zeros of Polynomial Functions (Presentation)

Polynomial Functions Zeros and Graphing Section 2-2

Section 2-3 Real Zeros of Polynomial Functions. Real Zeros of Polynomial Functions What you should know: 1. How to divide polynomials by other polynomials

Polynomial, Power, and Rational · PDF filePolynomial, Power, and Rational Functions ... 2.4 Real Zeros of Polynomial Functions 2.5 Complex Zeros and the Fundamental Theorem of Algebra

Polynomial functions start real zeros

171S4.4p Theorems about Zeros of Polynomial …cfcc.edu/faculty/cmoore/171ClassNotesFa12/171S4.4p.pdf171S4.4p Theorems about Zeros of Polynomial Functions 4 November 01, 2012 Oct 25

Real Zeros of Polynomial Functions - WCDE

Section 3.6 The Real Zeros of a Polynomial Function

Section 5.5 The Real Zeros of a Polynomial Function

Section 2.5 Zeros of Polynomial Functions Objectives

Zeros of Polynomial Functions€¦ · Zeros of Polynomial Functions Lesson 2-4 Objectives: 1. Use the Fundamental Theorem of Algebra to determine the number of zeros of polynomial

7.5.1 Zeros of Polynomial Functions 7.5.1 Zeros of Polynomial Functions Objectives: Use the Rational Root Theorem to find the zeros of a polynomial function

2.3 Real Zeros of Polynomial Functions 2015 Digital Lesson

Zeros of Polynomial Functions Advanced Math Section 3.4

3.3 - 1 3.3 Zero of Polynomial Functions Factor Theorem Rational Zeros Theorem Number of Zeros Conjugate Zeros Theorem Finding Zeros of a Polynomial Function

3.3 Real Zeros of Polynomial Functions - Franklin Universitycs.franklin.edu/~sieberth/MATH160/bookFiles/Chapter3/... · · 2006-12-273.3 Real Zeros of Polynomial Functions ... f

Section 2.5 Zeros of Polynomial Functions Objectivesteachers.dadeschools.net/lberkson/Documents/Ch2_Section5.pdfSection 2.5 Zeros of Polynomial Functions 327 Study Tip Be sure you

1 5.6 Complex Zeros; Fundamental Theorem of Algebra In this section, we will study the following topics: Conjugate Pairs Theorem Finding a polynomial function

Finding Zeros Given the Graph of a Polynomial Function Chapter 5.6

The Zeros of a Polynomial Function

Section 2.5 Zeros of Polynomial Functions of Polynomial... · Section 2.5 Zeros of Polynomial Functions The Rational Zero Theorem Example List all possible rational zeros of f(x)=x3-3x2-4x+12

3.6 The Real Zeros of Polynomial Functions Goals: Finding zeros of polynomials Factoring polynomials completely

Powerpoint Jeopardy Quadratic & Polynomial Functions & Models Rational Functions & Models Polynomial & Rational Inequalities Real Zeros of a Polynomial

College Algebra and Trigonometry€¦ · Zeros Polynomial Models Summary Exercises on Polynomial Functions, Zeros, and Graphs 378 3.5 Rational Functions: Graphs, Applications, and

Zeros of Polynomial Functions Objectives: 1. Use the Fundamental Theorem of Algebra to determine the number of zeros of polynomial functions 2. Find rational

SECTION 3.5 REAL ZEROS OF A POLYNOMIAL FUNCTION REAL ZEROS OF A POLYNOMIAL FUNCTION

2.4 – Real Zeros of Polynomial Functions

2.32.3 Real Zeros of Polynomial Functions. Quick Review

Zeros of Polynomial Functions

Chapter 3.3 Zeros of Polynomial Functionsinstructorcortez.com/Chapter3.3EricSolved.pdf · Chapter 3.3 – Zeros of Polynomial Functions Factoring Polynomials Sample Problem: Factor

Chapter 3 Section 3.3 Real Zeros of Polynomial Functions

INEQUALITIES FOR POLYNOMIAL ZEROS

2.5 Zeros of Polynomial Functions Notessevillaj.weebly.com/uploads/7/7/8/4/7784014/2.5_zeros_of...2.5 Zeros of Polynomial Functions Popularizers of mathematics are sharing bizarre

2.5 Zeros of Polynomial Functions€¦ · 2.5 Zeros of Polynomial Functions The Fundamental Theorem of Algebra If is a polynomial of degree where then has at least one zero in the