Presentation is loading. Please wait.

Presentation is loading. Please wait.

LESSON 5.6 Rational Zeros of Polynomial Functions.

Published byJulian Wilson Modified over 8 years ago

Similar presentations

Presentation on theme: "LESSON 5.6 Rational Zeros of Polynomial Functions."— Presentation transcript:

1 LESSON 5.6 Rational Zeros of Polynomial Functions

2 Solve x 3 – 5x 2 + 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 x 3 – 5x 2 + 8x – 4 = (x – 1)( ). Use synthetic division to find the missing factor. The missing factor is x 2 – 4x + 4, which can be factored. So solve and learn that x = 2. So the solutions are 1 and 2 (double root).

3 But what if you don’t know any zeros and cannot factor a polynomial? Rational Zero Theorem To 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) = 2x 3 + 3x 2 – 4x + 6. Answer: ±1,±2,±3,±6,±1/2,±3/2

4 Now try this one…. a)Solve x 3 + 4x 2 + x – 6 = 0 Answer: x = 1, x = -2, x = -3 Do they all check? Why do you think there were 3 solutions?

5 and this one… b) Find all of the roots of f(x) = x 4 + 2x 3 – 7x 2 – 20x – 12 Answer: x = 3, -2 (double root) and -1. Verify this using your graphing calculator.

6 and one last problem! c) Find the zeros of f(x) = 6x 4 – 25x 3 + 30x 2 – 5x – 6 How many answers should there be? Answer: x = 1, x = 2, x = 3/2, x = -1/3

Download ppt "LESSON 5.6 Rational Zeros of Polynomial Functions."

Similar presentations

Lesson 3.4 – Zeros of Polynomial Functions Rational Zero Theorem

Lesson 3.4 – Zeros of Polynomial Functions Rational Zero Theorem
$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.
Problem of the Day. Division and Rational Root Theorem TS: Making decisions after reflection and review Obj: Review polynomial division and how to find.

Problem of the Day. Division and Rational Root Theorem TS: Making decisions after reflection and review Obj: Review polynomial division and how to find.
5.5: Polynomial Long Division and Synthetic Division

5.5: Polynomial Long Division and Synthetic Division
EXAMPLE 2 Find the zeros of a polynomial function

EXAMPLE 2 Find the zeros of a polynomial function
OBJECTIVE: I will be able to calculate the real zeros of a polynomial function using synthetic division and the Rational Zero Theorem through use of in-class.

OBJECTIVE: I will be able to calculate the real zeros of a polynomial function using synthetic division and the Rational Zero Theorem through use of in-class.
EXAMPLE 2 Find all zeros of f (x) = x 5 – 4x 4 + 4x 3 + 10x 2 – 13x – 14. SOLUTION STEP 1 Find the rational zeros of f. Because f is a polynomial 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.

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!

Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!
EXAMPLE 2 Find all real zeros of f (x) = x 3 – 8x 2 +11x + 20. SOLUTION List the possible rational zeros. The leading coefficient is 1 and the constant.

EXAMPLE 2 Find all real zeros of f (x) = x 3 – 8x 2 +11x SOLUTION List the possible rational zeros. The leading coefficient is 1 and the constant.
Lesson 2.5 The Fundamental Theorem of Algebra. For f(x) where n > 0, there is at least one zero in the complex number system Complex → real and imaginary.

Lesson 2.5 The Fundamental Theorem of Algebra. For f(x) where n > 0, there is at least one zero in the complex number system Complex → real and imaginary.
Zeros of Polynomials PolynomialType of Coefficient 5x 3 + 3x 2 + (2 + 4i) + icomplex 5x 3 + 3x 2 + √2x – πreal 5x 3 + 3x 2 + ½ x – ⅜rational 5x 3 + 3x.

Zeros of Polynomials PolynomialType of Coefficient 5x 3 + 3x 2 + (2 + 4i) + icomplex 5x 3 + 3x 2 + √2x – πreal 5x 3 + 3x 2 + ½ x – ⅜rational 5x 3 + 3x.
Finding Rational Zeros.

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

The Rational Zero Theorem The Rational Zero Theorem gives a list of possible rational zeros of a polynomial function. Equivalently, the theorem gives all.
Using Technology to Approximate Roots of Polynomial Equations.

Using Technology to Approximate Roots of Polynomial Equations.
Finding Real Roots of Polynomial Equations

Finding Real Roots of Polynomial Equations
Quick Crisp Review Zeros of a polynomial function are where the x-intercepts or solutions when you set the equation equal to zero. Synthetic and long division.

Quick Crisp Review Zeros of a polynomial function are where the x-intercepts or solutions when you set the equation equal to zero. Synthetic and long division.
2.3 Real Zeros of Polynomial Functions 2015 Digital Lesson.

2.3 Real Zeros of Polynomial Functions 2015 Digital Lesson.
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.

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.
2.4 – Real Zeros of Polynomial Functions

2.4 – Real Zeros of Polynomial Functions

Similar presentations

Ads by Google