Review SYNTHETIC DIVISION to find roots of third degree characteristic polynomial Pamela Leutwyler.

Slides:

Advertisements

Similar presentations

4.4 Rational Root Theorem.

Advertisements

Rational Root Theorem.

4.4 Notes The Rational Root Theorem. 4.4 Notes To solve a polynomial equation, begin by getting the equation in standard form set equal to zero. Then.

EXAMPLE 2 Find the zeros of a polynomial function

Section 5.5 – The Real Zeros of a Rational Function

EXAMPLE 2 Find all zeros of f (x) = x 5 – 4x 4 + 4x x 2 – 13x – 14. SOLUTION STEP 1 Find the rational zeros of f. Because f is a polynomial function.

Objective Video Example by Mrs. G Give It a Try Lesson 6.6  Find the rational and real zeros of a polynomial function.

Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!

C. Higher Functions Pre-Calculus 30.

The Remainder and Factor Theorems Check for Understanding 2.3 – Factor polynomials using a variety of methods including the factor theorem, synthetic division,

The Rational Zero Theorem The Rational Zero Theorem gives a list of possible rational zeros of a polynomial function. Equivalently, the theorem gives all.

Bell Ringer 1. What is the Rational Root Theorem (search your notebook…Unit 2). 2. What is the Fundamental Theorem of Algebra (search your notebook…Unit.

2.3 Synthetic Substitution OBJ:  To evaluate a polynomial for given values of its variables using synthetic substitution.

Factor Theorem & Rational Root Theorem

Rational Root Theorem By: Yu, Juan, Emily. What Is It? It is a theorem used to provide a complete list of all of the possible rational roots of the polynomial.

7.5.1 Zeros of Polynomial Functions

Using Technology to Approximate Roots of Polynomial Equations.

Finding Real Roots of Polynomial Equations

6.6 The Fundamental Theorem of Algebra

Lesson 2-6 Solving Polynomial Equations by Factoring – Part 2.

6-5 Theorems About Roots of Polynomial Equations

5.5 Theorems about Roots of Polynomial Equations P

6.9 Rational Zero Theorem Parts of a polynomial function f(x) oFactors of the leading coefficient = q oFactors of the constant = p oPossible rational roots.

Section 3.3 Theorems about Zeros of Polynomial Functions.

Warm Up. Find all zeros. Graph.. TouchesThrough More on Rational Root Theorem.

Sec. 6-5: Theorems About Roots of Polynomial Equations.

Section 5.5 The Real Zeros of a Polynomial Function.

Theorems About Roots of Polynomial Equations. Find all zeros: f(x)= x +x –x Synthetic Division one zero…need 2 more use (x – k), where.

By Ms. Tang. We’ve learned how to solve quadratics (which is a type of polynomials) by: Factoring Completing the square Quadratic formula.

Solving Polynomials. What does it mean to solve an equation?

Solving Polynomial Equations by Factoring Factoring by grouping Ex. 1. Solve:

6.5 Theorems About Roots of Polynomial Equations

6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a.

LESSON 5.6 Rational Zeros of Polynomial Functions.

9.8 Day 2 – Finding Rational Zeros. The Rational Zero Theorem: If has integer coefficients, then every rational zero of f have the following form:

Solving polynomial equations

Warm Up: 1.  2 Finding Rational Zeros (Day 1) 3.

Solving Polynomials. Factoring Options 1.GCF Factoring (take-out a common term) 2.Sum or Difference of Cubes 3.Factor by Grouping 4.U Substitution 5.Polynomial.

Polynomials. DegreeNameExample 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic Some of the Special Names of the Polynomials of the first few degrees:

Pamela Leutwyler. Find the eigenvalues and eigenvectors next.

STD 3: To divide polynomials using long division and synthetic division and the rational root theorem Warm Up /15.

Algebra 2 List all the integer factors for the number below: 36.

Zeros (Solutions) Real Zeros Rational or Irrational Zeros Complex Zeros Complex Number and its Conjugate.

Dividing Polynomials Two options: Long Division Synthetic Division.

Warm-ups Week 8 10/8/12 Find the zeros of f(x) = x3 + 2x2 – 13x + 10 algebraically (without a graphing calculator). What if I told.

Polynomial Long Division Review

Factor Theorem & Rational Root Theorem

Roots and Zeros 5.7.

Algebra II with Trigonometry Ms. Lee

Notes Over 3.4 The Rational Zero Test

5.8 Rational Zero Theorem.

Real Zeros Intro - Chapter 4.2.

4.2 Real Zeros Finding the real zeros of a polynomial f(x) is the same as solving the related polynomial equation, f(x) = 0. Zero, solution, root.

5-5 Theorems About Roots of Polynomial Equations

Rational Root Theorem Math 3 MM3A1.

Finding Zeros of Polynomials

Precalculus PreAP/Dual, Revised ©2017

Finding Roots of Higher Order Polynomials

Section 3.4 Zeros of Polynomial Functions

Find all solutions of the polynomial equation by factoring and using the quadratic formula. x = 0 {image}

Zeros to Quadratic Functions

Warm-up Complete this as a group on you Board. You have 15 minutes

Factor Theorem & Rational Root Theorem

Finding Zeros of Polynomials

Factor Theorem & Rational Root Theorem

“You wasted $150,000 on an education you coulda got for $1

4.3 – The Remainder and Factor Theorems

Polynomial and Rational Functions

Section 2.4: Real Zeros of Polynomial Functions

The Real Zeros of a Polynomial Function

Presentation transcript:

Review SYNTHETIC DIVISION to find roots of third degree characteristic polynomial Pamela Leutwyler

(2x – 5)(x + 3)(7x – 2) =

14x 3 + 3x 2 – 107x + 30 = 0

(2x – 5)(x + 3)(7x – 2) = 14x 3 + 3x 2 – 107x + 30 = 0 The roots are: -3

(2x – 5)(1x + 3)(7x – 2) = 14x 3 + 3x 2 – 107x + 30 = 0 The roots are: -3

(2x – 5)(1x + 3)(7x – 2) = 14x 3 + 3x 2 – 107x + 30 = 0 The roots are: -3

(2x – 5)(1x + 3)(7x – 2) = 14x 3 + 3x 2 – 107x + 30 = 0 The roots are: -3 If is a root of the polynomial equation

(2x – 5)(1x + 3)(7x – 2) = 14x 3 + 3x 2 – 107x + 30 = 0 The roots are: -3 If is a root of the polynomial equation Then q is a factor of

(2x – 5)(1x + 3)(7x – 2) = 14x 3 + 3x 2 – 107x + 30 = 0 The roots are: -3 If is a root of the polynomial equation Then q is a factor of 14 and p is a factor of

A characteristic polynomial will always have lead coefficient = 1. Rational eigenvalues will be integral factors of the constant coefficient of the characteristic polynomial. example: find the eigenvalues for the matrix potential rational roots are factors of , -1, +2, -2, +7, -7, +14, -14

potential rational roots are factors of , -1, +2, -2, +7, -7, +14, -14 Test the potrats using synthetic division: 

potential rational roots are factors of , -1, +2, -2, +7, -7, +14, -14 Test the potrats using synthetic division: +1  The remainder is NOT ZERO. +1 is not a root.

potential rational roots are factors of , -1, +2, -2, +7, -7, +14, -14 Test the potrats using synthetic division: +7  The remainder is ZERO. +7 is a root.

potential rational roots are factors of , -1, +2, -2, +7, -7, +14, -14 Test the potrats using synthetic division: +7  The remainder is ZERO. +7 is a root. factor this or use quadratic formula or continue with synthetic division to get the other roots.