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Algebra 2 5-5 Complete Lesson: Theorems About Roots of Polynomial Equations

Last updated over 4 years ago

22 questions

Note from the author:

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A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Question 1

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Solve It! I am greater than my square. The sum of my numerator and denominator is 5. What fraction am I?

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Question 6

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Question 7

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Question 13

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Question 14

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Question 15

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Question 16

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Question 17

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Question 18

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Question 19

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Question 20

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Question 21

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Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Question 22

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Reflection: Math Success

Question 2

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Question 3

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Question 4

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Question 5

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Problem 5 Got It? Identify the statements that can be made using Descartes' Rule of Signs regarding the function. 

There is one negative real root.

There are two negative real roots.

There are one or three positive real roots.

There are two or four positive real roots.

According to Descartes' Rule of Signs:

Problem 5 Got It? Reasoning: Can you confirm real and complex roots graphically? Explain. Identify the true statements below.

Real roots can be confirmed graphically, because they are the x-intercepts.

Complex roots can be confirmed graphically, because they are the y-intercepts.

Complex roots cannot be confirmed graphically, because they have an imaginary component.

Real roots cannot be confirmed graphically, because they are not associated with x-intercepts.

Question 8

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Question 9

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Question 10

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Question 11

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Question 12

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Vocabulary: Drag a complex number from the left to create a conjugate pair.

Reasoning: In the statement below, r and s represent integers. Is the statement always, sometimes, or never true?

Always

Sometimes

Never

Reasoning: In the statement below, r and s represent integers. Is the statement always, sometimes, or never true?

Always

Sometimes

Never

Review Lesson 5-4: Match each expression on the left with its quotient on the right.

Review Lesson 5-1: Consider the standard form of each polynomial. Then classify it by its degree AND number of terms.

monomial

binomial

trinomial

polynomial of four terms

constant

linear

quadratic

cubic

quartic

quintic

Use Your Vocabulary: True or False? 1 and -1 are roots of the equation. 

True

False

Use Your Vocabulary: True or False? The equation has roots 4 and -4. 

True

False

Use Your Vocabulary: Identify the number of roots each polynomial has.

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Problem 1 Got It?

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Problem 2 Got It?

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Problem 3 Got It?

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Problem 4 Got It? 
HINT: you will need to multiply factors derived from the given roots, including (x - (2 - 3i)) and (x - (2 + 3i)).

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