Warm-up Find the solutions to the polynomial equation.

Slides:



Advertisements
Similar presentations
4.4 Rational Root Theorem.
Advertisements

Notes 6.6 Fundamental Theorem of Algebra
Rational Root Theorem.
2.4 – Zeros of Polynomial Functions
Zeros of Polynomial Functions
Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!
2.8 - Solving Equations in One Variable. By the end of today you should be able to……. Solve Rational Equations Eliminate Extraneous solutions Solve Polynomial.
Warm up Use the Rational Root Theorem to determine the Roots of : x³ – 5x² + 8x – 6 = 0.
Objectives Fundamental Theorem of Algebra 6-6
Section 6-2: Polynomials and Linear Factors
Warm-up Find the quotient Section 6-4: Solving Polynomial Equations by Factoring Goal 1.03: Operate with algebraic expressions (polynomial,
Warm-up Given these solutions below: write the equation of the polynomial: 1. {-1, 2, ½)
Warm-up 1.The height of a cube is set at (x + 1). Find the polynomial that represents the volume of the cube. 2.A rectangular swimming pool is three times.
The Rational Root Theorem.  Is a useful way to find your initial guess when you are trying to find the zeroes (roots) of the polynomial.  THIS IS JUST.
The Rational Root Theorem The Rational Root Theorem gives us a tool to predict the Values of Rational Roots:
6.6 The Fundamental Theorem of Algebra
7.5 Zeros of Polynomial Functions Objectives: Use the Rational Root Theorem and the Complex Conjugate Root Theorem. Use the Fundamental Theorem to write.
Rational Root and Complex Conjugates Theorem. Rational Root Theorem Used to find possible rational roots (solutions) to a polynomial Possible Roots :
7.6 Rational Zero Theorem Algebra II w/ trig. RATIONAL ZERO THEOREM: If a polynomial has integer coefficients, then the possible rational zeros must be.
Warm-up p 499 check skills (1 – 12). Quiz 1.If z=30 when x=3 and y=2, write the function that models the relationship “z varies directly with x and inversely.
Section 1-4: Solving Inequalities Goal 1.03: Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems.
Using the Fundamental Theorem of Algebra 6.7. Learning Targets Students should be able to… -Use fundamental theorem of algebra to determine the number.
Section 5.5 The Real Zeros of a Polynomial Function.
Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Additional Example 2A: Solving Equations with Fractions = – 3737 n
Fundamental Theorem of Algebra TS: Demonstrating understanding of concepts Warm-Up: T or F: A cubic function has at least one real root. T or F: A polynomial.
Objective: To learn & apply the fundamental theorem of algebra & determine the roots of polynomail equations.
Warm-Up: Solve each equation. Essential Question  How do I use the quadratic formula?
Algebra Rational Algebraic Expressions. WARMUP Simplify:
Radical expressions, rational exponents and radical equations ALGEBRA.
PreCalculus Section P.1 Solving Equations. Equations and Solutions of Equations An equation that is true for every real number in the domain of the variable.
Warmup Divide using synthetic division using the zero given. Then factor the answer equation completely and solve for the remaining zeroes. Show.
Solving Polynomials.
Holt McDougal Algebra 2 Fundamental Theorem of Algebra How do we use the Fundamental Theorem of Algebra and its corollary to write a polynomial equation.
Warm-Up 2/26 1. J. Rigor: You will learn how to find the real and complex zeros of polynomial functions. Relevance: You will be able to use graphs and.
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.
Ch. 6.4 Solving Polynomial Equations. Sum and Difference of Cubes.
HW Warm-Up Evaluate the expression. HW Lesson 9.1: Solving Quadratic Equations by Finding Square Roots Algebra I.
Algebra Finding Real Roots of Polynomial Equations.
Algebra 2. Solve for x Algebra 2 (KEEP IN MIND THAT A COMPLEX NUMBER CAN BE REAL IF THE IMAGINARY PART OF THE COMPLEX ROOT IS ZERO!) Lesson 6-6 The Fundamental.
HOMEWORK CHECK.
Chapter 6 Polynomials Review
Adding and Subtracting Rational Expressions
10.4 Solving Factored Polynomial Equations
Rational Root Theorem and Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra
Rational Zero Theorem Rational Zero Th’m: If the polynomial
Rational Root and Complex Conjugates Theorem
Rational Root Theorem and Fundamental Theorem of Algebra
Finding Real Roots of Polynomial Equations
Lesson 7.2: Finding Complex Solutions of Polynomial Equations
7.5 Zeros of Polynomial Functions
M3U5D5 Warmup Simplify the expression.
Complex Numbers and Roots
If a polynomial q(x) is divided by x – 4, the quotient is 2
Solving Polynomial Inequalities
Zeros of a Polynomial Function
Apply the Fundamental Theorem of Algebra
Lesson: _____ Section 2.5 The Fundamental Theorem of Algebra
Rational Root Theorem.
Algebra Section 11-1 : Rational Expressions and Functions
Warmup Find the exact value. 1. √27 2. –√
5.4 – Complex Numbers.
Warm Up The area of a rectangle is expressed by the polynomial
Fundamental Theorem of Algebra
Find a if: a2 + b2 = c2 1.) c=10, b= 8 2.) c=20,b=16 3.) a2+152=172
3.6 Solve Quadratics by Finding Square Roots
Directions- Solve the operations for the complex numbers.
Objective SWBAT solve polynomial equations in factored form.
Fundamental Theorem of Algebra Roots/Zeros/X-Intercepts
Presentation transcript:

Warm-up Find the solutions to the polynomial equation.

Classwork: #1, 6, 10,11, 13, 14, 19, 20, 21, 26, 27, 30

Section 6-5: Theorems about Roots of Polynomial Equations Goal 1.02: Define and compute with complex numbers. Goal 1.03: Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems.

Find a polynomial equation with the given roots ex1: – 4, 4i - 4i must also be a zero (x + 4)(x – 4i)(x + 4i) (x + 4)(x 2 + 4i – 4i – 16i 2 ) (x + 4)(x ) x x + 4x x 3 + 4x x + 64 ex2: - 1, 3 + i, 3 – i must also be a zero (x + 1)[x – (3 + i)][x – (3 – i)] (x + 1)(x – 3 – i)(x – 3 + i) (x + 1)(x 2 – 3x + xi – 3x + 9 – 3i – xi + 3i – i 2 ) (x + 1)(x 2 – 6x + 10) x 3 – 6x x + x 2 – 6x + 10 x 3 – 5x 2 + 2x + 10

ex3: 6, 3 – 2i 3 + 2i must also be a zero (x – 6 )[x – (3 – 2i)][x – (3 + 2i)] (x – 6 )(x – 3 + 2i)(x – 3 – 2i) (x – 6 )(x 2 – 3x – 2xi – 3x i + 2xi – 6i – 4i 2 ) (x – 6 )(x 2 – 6x + 13) x 3 – 6x x – 6x x – 78 x 3 – 12x x – 78 ex4: 1,  6 -  6 must also be a zero (x – 1)(x -  6)(x +  6) (x – 1)(x 2 +  6x -  6x -  36) (x – 1)(x 2 – 6) x 3 – 6x – x x 3 – x 2 – 6x + 6

Extra Example

Classwork/ Homework Study for 15 minutes each day this weekend.