WARM UP.

Slides:



Advertisements
Similar presentations
Notes 6.6 Fundamental Theorem of Algebra
Advertisements

Bell Problem Factor the polynomial completely given that x – 4 is a factor: f(x) = x3 – x2 – 22x + 40.
TODAY IN ALGEBRA…  Warm up: Find products of special polynomials  Learning Target: 9.4 You will solve polynomial equations in factored form  Independent.
Bell Problem Find the real number solutions of the equation: 18x 3 = 50x.
Objectives Fundamental Theorem of Algebra 6-6
5.7 Apply the Fundamental Theorem of Algebra
Lesson 4-1 Polynomial Functions.
Do Now: Find all real zeros of the function.
Today in Pre-Calculus Go over homework Notes: Remainder and Factor Theorems Homework.
2.7 Apply the Fundamental Theorem of Algebra Polynomials Quiz: Tomorrow (over factoring and Long/Synthetic Division) Polynomials Test: Friday.
7.3 Products and Factors of Polynomials Objectives: Multiply polynomials, and divide one polynomial by another by using long division and synthetic division.
WARM UP. Homework Q’s Dividing Polynomials using Synthetic Division EQ: How is Long Division utilized to divide a polynomial functions? Assessment:
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.
1 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. Start Up Day 13 Find all zeros of the given function:
7.5 Roots and Zeros Objectives: The student will be able to…
WARM UP 1. Factor the polynomial completely. 27 – y 3 2. What are the real number solutions of the equation 2x = x 2 + x 3 ?
Copyright © 2011 Pearson, Inc. 2.5 Complex Zeros and the Fundamental Theorem of Algebra.
5.6 The Fundamental Theorem of Algebra. If P(x) is a polynomial of degree n where n > 1, then P(x) = 0 has exactly n roots, including multiple and complex.
Section 4.6 Complex Zeros; Fundamental Theorem of Algebra.
Holt McDougal Algebra Fundamental Theorem of Algebra Use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation of least.
Solving Polynomials.
7.5 Roots and Zeros Objectives:
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.
Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA.
WARM UP Multiply the polynomial. 1. (x + 2)(x + 3) 2. (2x – 1)(2x + 1) 3. (x – 7) 2 4.3x 2 (x + 5)
Algebra Finding Real Roots of Polynomial Equations.
Divide by x - 1 Synthetic Division: a much faster way!
Fundamental Theorem of Algebra
Section 6.6 The Fundamental Theorem of Algebra
Complex Zeros and the Fundamental Theorem of Algebra
Solving Polynomial Functions
Fundamental Theorem of Algebra
Rational Root and Complex Conjugates Theorem
Finding Real Roots of Polynomial Equations
Lesson 7.2: Finding Complex Solutions of Polynomial Equations
3.8 Complex Zeros; Fundamental Theorem of Algebra
WARM UP Evaluate without using a calculator. 1. √ –2
The Fundamental Theorem of Algebra
Finding Zeros of Polynomials
Warm Up Identify all the real roots of each equation.
WARM UP.
WARM UP Find all real zeros of the functions
6-8 Roots and Zeros – Day 1 SWBAT
Warm Up - September 27, 2017 Classify each polynomial by degree and by number of terms. 1. 5x x2 + 4x - 2 Write each polynomial in standard form.
Zeros of a Polynomial Function
Today in Precalculus Go over homework Notes: Remainder
Apply the Fundamental Theorem of Algebra
Fundamental Theorem of Algebra
Lesson: _____ Section 2.5 The Fundamental Theorem of Algebra
Warm-up 1. Solve the system of equations 3x + 2y = 12 and x – y = – 1 graphically. 2. Solve the system. Then classify the system as consistent and independent,
WARM UP Simplify each expression. 1. (–2) – 34.
Warm Up Graph
Warm Up The area of a rectangle is expressed by the polynomial
Fundamental Theorem of Algebra
Use synthetic substitution to evaluate
WARM UP Evaluate the expression Simplify the Expression
If you got an A you have a star on the Wall with your name Congrat’s!
Warm Up 1) Find f(-3) for
Warm Up Graph f(x) = 3x – 2 using a table
Apply the Fundamental Theorem of Algebra
Chapter 4 – Polynomial and Rational Functions
8-5 Rational Zero Theorem
6-8 Roots and Zeros Given a polynomial function f(x), the following are all equivalent: c is a zero of the polynomial function f(x). x – c is a factor.
Ch 3.1: Solving Quadratic Equations
Bellwork Solve the Polynomial Equation by Factoring
5.8 Analyzing Graphs of Polynomials
WARM UP.
Fundamental Theorem of Algebra Roots/Zeros/X-Intercepts
Presentation transcript:

WARM UP

Introduction to Finding all Zeros EQ: How do we use the Fundamental Theorem of Algebra and it’s corollary to find the zeros of a polynomial? Assessment: Students will write a summary on ways to use the Fundamental Theorem of Algebra to find the zeros of a polynomial.

Key Term When a solution appears more than once this called a _______________. repeated solution ** Note: For the equation f(x) = 0, k is a repeated solution if and only if the factor (x – k) has a degree greater than 1 when f is factored.

KEY CONCEPT > one n 2 3

Find the number of solutions and zeros a. How many solutions does the equation x3 + 5x2 + 4x + 20 = 0 have? b. How many zeros does the function f (x) = x4 – 8x3 + 18x2 – 27 have?

Beginning to find all Zeros DO NOT WRITE DOWN Ex. Find all Zeros f (x) = x4 – 8x3 + 18x2 – 27

You Try It! 1. How many solutions does the equation x4 + 5x2 – 36 = 0 have? 2. How many zeros does the function f (x) = x3 + 7x2 + 8x – 16 have?

Homework Textbook - Pg. 383 #3-9