Solving Polynomial Functions

Slides:

Advertisements

Similar presentations

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1 Homework, Page 234 Write the polynomial in standard form, and.

Advertisements

3-5 Finding the real roots of polynomial Equations

CHAPTER 7-1 SOLVING SYSTEM OF EQUATIONS. WARM UP  Graph the following linear functions:  Y = 2x + 2  Y = 1/2x – 3  Y = -x - 1.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Real Zeros of a Polynomial Function Objectives: Solve Polynomial Equations. Apply Descartes Rule Find a polynomial Equation given the zeros.

OUTLINE  Homework (and homework questions)  Ask any review questions you want  Review long division, solve by factoring and graphing calculators  BREAK.

1 Using the Fundamental Theorem of Algebra.  Talk about #56 & #58 from homework!!!  56 = has -1 as an answer twice  58 = when you go to solve x 2 +

3.1 Solving equations by Graphing System of equations Consistent vs. Inconsistent Independent vs. Dependent.

Chapter 2: Equations and Inequalities

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

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

Topic: U4L5 Remainder and Factor Theorems EQ: Can I correctly apply the Remainder and Factor Theorems to help me factor higher order polynomials?

Solving equations with polynomials – part 2. n² -7n -30 = 0 ( )( )n n 1 · 30 2 · 15 3 · 10 5 · n + 3 = 0 n – 10 = n = -3n = 10 =

Warmup  1.) 4x 2 = 202.) 3x = 29  3.)4.)  5.)6.)

Quadratic Equations: Factoring, Square Root Methods.

By the end of this section, you will be able to: 1. Determine the number and type of roots for a polynomial equation; 2. Find the zeros of a polynomial.

Remainder and Factor Theorems

Review: 6.5e Mini-Quiz 1. Solve: 16x 2 – 24x = – 4x Solve: (x – 3)(x – 2) = 30.

The Fundamental Theorem of Algebra It’s in Sec. 2.6a!!! Homework: p odd, all.

Specialist Mathematics Polynomials Week 3. Graphs of Cubic Polynomials.

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.

Section 6: Fundamental Theorem of Algebra Use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation of least degree with.

Determine the number and type of roots for a polynomial equation

Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA.

Precalculus Section 2.5 Approximate real roots of polynomials using graphing calculators Note: The solution to x 2 + 2x – 8 = 0 is found by (x+4)(x-2)

6.5 The Quadratic Formula and the Discriminant

Using Intercepts.

HOMEWORK CHECK.

Chapter 6 Polynomials Review

Solving Polynomial Equations

Objectives Find x- and y-intercepts and interpret their meanings in real-world situations. Use x- and y-intercepts to graph lines.

ALGEBRA 1 CHAPTER 7 LESSON 5 SOLVE SPECIAL TYPES OF LINEAR SYSTEMS.

Roots and Zeros 5.7.

When solving #30 and #34 on page 156, you must “complete the square.”

Daily Check!!!.

Daily Check!!! (Irrational Roots)

Bell Ringer 1. What is the Rational Root Theorem

Finding Real Roots of Polynomial Equations

Lesson 2.5 The Fundamental Theorem of Algebra

Daily Check!!!.

9.3 Solving Quadratic Equations

SECTION 9-3 : SOLVING QUADRATIC EQUATIONS

If a polynomial q(x) is divided by x – 4, the quotient is 2

**Get signed by your parents for 5 bonus points on the test!!

Warm Up Test Friday HW- Solving Quadratics Worksheet.

1. Use the quadratic formula to find all real zeros of the second-degree polynomial

Solving Polynomial Equations

Graphing Nonlinear Inequalities

Monomials & Polynomials

Main Ideas Key Terms Chapter 2 Section 3 Graphing a Polynomial

Homework Check.

Homework Check.

Chapter 6, Sections 1 & 2 Quadratic Functions.

P.1 Graphs and Models.

Common Logs & Natural Logs

Solving Systems of Equations Using Matrices

Polynomial Functions Chapter 7, Sections 1 and 2.

Dividing Polynomials Chapter 5, Section 3.

Logarithmic Functions

Graphs of Quadratic Functions

Solving Special Cases.

Graphs of Quadratic Functions

Chapter 6, Section 5 Quadratic Formula.

Bellwork Solve the Polynomial Equation by Factoring

Objective SWBAT solve polynomial equations in factored form.

Intersection Method of Solution

Fundamental Theorem of Algebra Roots/Zeros/X-Intercepts

Presentation transcript:

Solving Polynomial Functions Chapter 7, Sections 3, 4, and 5

A few things to remember: Most solutions can be found by graphing and finding the intersections. SOLUTIONS = ROOTS = ZEROS = X- INTERCEPTS!!!! Complex answers ALWAYS come in pairs, which are conjugates. The number of solutions is the same as the degree of the polynomial “a” is the answer if and only if f(a) = 0

Solving Polynomials with Real Solutions

What happens when all answers aren’t real????? Recall: The number of solutions is the degree of the polynomial Complex solutions come in pairs Examples of describing the types of solutions: Polynomial Deg. MAX Sol. # Real #Complex

Finding factors using solutions If you know the solution to a polynomial function, then you know a factor. For example: If x=3 is a solution, then x-3 is a factor. If x=-9 is a solution, then x+9 is a factor. If x=2/3 is a solution, then 2x-3 is a factor. If x=-3/4 is a solution, then 4x+3 is a factor.

Using solutions to get the equation If you know the solutions, then you can determine the original equation. For example: Solutions are 2 and 3: Solutions are 4i and -4i: Solutions are -3, 5, and -2: Solution is 3+i

Homework Pages 45 in workbook Page 46 in workbook Page 47 in workbook Problems 10-24 even (give the real answers and how many complex answers) Page 46 in workbook Problems 17-27 odd (find the answers and then use that to find the factors) Page 47 in workbook Problems 17-20 Exit Slip Explain how the solutions relate to the equation of the polynomial.