6.5 finding real roots of polynomial equations. -factoring to find real roots -explain multiplicity...

6.5 Finding Real Roots of Polynomial Equations

Upload: sheena-walton

Post on 02-Jan-2016

229 views

Category:

Documents

0 download

Report

Download

Embed Size (px):

TRANSCRIPT

6.5

Finding Real Roots of Polynomial Equations

-factoring to find real roots-explain Multiplicity

The root 0 has a multiplicity of 3.The root -3 has a multiplicity of 2.

5 4 33 18 27 0x x x

Page 3: 6.5 Finding Real Roots of Polynomial Equations. -factoring to find real roots -explain Multiplicity A. The root 0 has a multiplicity of 3. The root -3

Multiple Roots

• Multiple roots appear in a polynomial equation that has a factor that appears more than once.

Graph on your calculator.

Notice where it touches the x-axis and what it looks like.

5 4 33 18 27 0x x x

Page 4: 6.5 Finding Real Roots of Polynomial Equations. -factoring to find real roots -explain Multiplicity A. The root 0 has a multiplicity of 3. The root -3

Rational Root Theorem

• Every rational root can be written in the form

• Where p is a factor of the constant term

• q is a factor of the leading coefficient.

Page 5: 6.5 Finding Real Roots of Polynomial Equations. -factoring to find real roots -explain Multiplicity A. The root 0 has a multiplicity of 3. The root -3

Rational Root Theorem

• Use the Rational Root Theorem to identify all possible rational roots.

3 23 2 1 0x x

Page 6: 6.5 Finding Real Roots of Polynomial Equations. -factoring to find real roots -explain Multiplicity A. The root 0 has a multiplicity of 3. The root -3

Rational Root Theorem

• Use the Rational Root Theorem to identify all possible rational roots.

32 10 0x x

Page 7: 6.5 Finding Real Roots of Polynomial Equations. -factoring to find real roots -explain Multiplicity A. The root 0 has a multiplicity of 3. The root -3

Find all the real roots of each equation.

• Steps:1. List all possible roots

2. Use synthetic division until you get to a quadratic equation

3. Write the factors ( ) ( )

4. Write the zeros

These steps MUST be shown on all problems!!!

Page 8: 6.5 Finding Real Roots of Polynomial Equations. -factoring to find real roots -explain Multiplicity A. The root 0 has a multiplicity of 3. The root -3

Find all real roots.3 23 4 17 6 0x x x

Page 9: 6.5 Finding Real Roots of Polynomial Equations. -factoring to find real roots -explain Multiplicity A. The root 0 has a multiplicity of 3. The root -3

Find all real roots.3 22 3 5 2 0x x x

Page 10: 6.5 Finding Real Roots of Polynomial Equations. -factoring to find real roots -explain Multiplicity A. The root 0 has a multiplicity of 3. The root -3

Find all real roots.4 3 24 7 34 24 0x x x x

Page 11: 6.5 Finding Real Roots of Polynomial Equations. -factoring to find real roots -explain Multiplicity A. The root 0 has a multiplicity of 3. The root -3

Homework

• Page 442 (2-9, 11-14)

Holt McDougal Algebra 2 Finding Real Roots of Polynomial Equations How do we identify the multiplicity of roots? How do we use the Rational Root Theorem

Vertical Root Fracture initiation in curved roots after ... · Vertical Root Fracture initiation in curved roots after root canal preparation: ... They have an off-centered rectangular

Square roots notes - Weebly€¦ · O ROOTS square root is known as the principle square root, and when using the sign, the solution is the positive square root. 1's = both Square

Root and Root Canal Morphology of Maxillary First Premolars ......maxillary ﬁrst premolars (56.6%) had 2 roots, 41.7% had 1 root, and 1.7% had 3 roots. The 3-rooted premolars had

Warm-Up Find the Square Root: 1)3) 2) 4). Estimate square roots. Simplify square roots. Objectives

Roots and Root Systems - University of Delaware

Roots and Soil Chapter 5. Outline Root Development Root Structure Specialized Roots Mycorrhizae Root Nodules Soils Horizons Soil Formation - Factors

02. Square Root and Cube Roots

Roots, Stems, and Leaves. Roots Types of roots –Taproot: primary root that grows longer and thicker than the secondary roots (grows deeper) ex. carrots

Monocot and Eudicot/Dicot Roots Eudicot/Dicot RootMonocot Root

Lab 6 Roots - Napa Valley College 6 Roots.pdf · The$primary$root$system$is$the$plant’s$interfacewith$its$physical$substrate ... Monocot$root.$ $ ... Lab 6 Roots Author: Joshua

Roots Fibrous RootsTap Root. 1 = emerging lateral root, 2 = lateral root primordium, 3 = root hair nearly fully grown, 4 = mature vessel element, 5 =

· contractile root (C RL = contractile root of lateral bulb), LB = lateral bulb, NR = nutrient roots (NRC = nutrient roots of lateral bulb), sh = shrinkage Bot. 106 (1993) Fig

8.1 Square Roots and the Pythagorean Theorem. Square Root

Root, Tubers & Bulbs Postharvest Handling Roots, Tubers, Bulbs

Roots I. Root characteristics A. Functions B. Root systems 1. fibrous root systems 2. tap root systems C. Food storage D. Examples II. Root growth A

Study of external structure. Primary root develops from radicle Produce secondary, tertiary roots etc Tap root system- primary roots and its branches

Angiosperms IV Primary Growth: Roots and Stems. Roots and Root Systems Root Systems are often classified as either: –TAP ROOT SYSTEMS (found most commonly

Objectives Identify the multiplicity of roots Use the Rational Root Theorem and the Irrational Root Theorem to solve polynomial equations

The Induction of Lateral Roots by Indoleacetic Acid and Root Decapitation … · 2018-09-18 · lateral root formation in isolated pea roots grown in nutrient culture. METHODS.-Methods

Sect. 7.1 Radical Expressions & Radical Functions Square Roots The Principal Square Root Square Roots of Expressions with Variables The Square Root

ROOT SYSTEMS. ROOT ORGANIZATION Roots systems are usually either: Tap root (dicots) or Fibrous root (monocots) some plants may have both; e.g. clover

Lesson 5 Contents Example 1Two Rational Roots Example 2One Rational Root Example 3Irrational Roots Example 4Complex Roots Example 5Describe Roots

Word Roots the Web's Largest Root Words and Prefix Director

MONOCOT ROOT - Building The Pridebuildingthepride.com/faculty/fjmenapace/bio460powpt/BI...MONOCOT ROOT ADVENTITIOUS ROOTS FIBROUS ROOT SYSTEM ^ ADVENTITIOUS ROOTS A ADVENTITIOUS ROOT

BMPs for Healthy Tree Roots in Urban Environments · –No circling roots, J-roots, girdling roots •Establish quickly with rapid root growth into the landscape soil –In ideal

Nature of Roots. > 0 Two unequal real roots = 0 One double real root (Two equal real roots) < 0 No real roots Note: 0 Real roots Quadratic Equation:

All About Plants. Name two types of roots. Tap root Fibrous root

Roots Leaves Stems Dicot RootMonocot Root

Holt McDougal Algebra 2 6-5 Finding Real Roots of Polynomial Equations Identify the multiplicity of roots. Use the Rational Root Theorem and the irrational

Polynomial Ideals Euclidean algorithm Multiplicity of roots Ideals in F[x]

2011. Roots Morphology Outline Definition characteristics of a root Why are roots important? Contributors to Root Growth Parts of a Root Regions of Root

3.5 The Expansion - part 2 - B3.notebook · 3.5 The Expansion part 2 B3.notebook 6 November 10, 2014 Nov 1010:18 AM Multiplicity (power of a root) If a root has an even multiplicity,

Holt McDougal Algebra 2 Finding Real Roots of Polynomial Equations Identify the multiplicity of roots. Use the Rational Root Theorem and the irrational

Chapter 5. Roots and Root Systems