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# Pre-Calculus - PowerPoint PPT Presentation

Pre-Calculus. Unit 7: Lesson 2: Polynomial Equations. Warm-Up. Study your notes. There will be a 5 question timed quiz and an exit ticket at the end of the period today. Topic/Objective:. I will learn how to find all possible solutions, rational or irrational. Essential Question:.

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### Pre-Calculus

Unit 7: Lesson 2:

Polynomial Equations

Study your notes.

There will be a 5 question timed quiz and an exit ticket at the end of the period today.

I will learn how to find all possible solutions, rational or irrational.

How do find all zeros in a polynomial equation?

Terminology Background:

• Real Roots:

• Physical x-intercepts

• Factors that are real numbers

• Numbers are rational

• Complex Roots:

• May not cross the x-axis

• Might have imaginary numbers

• Might have irrational or rational numbers

Terminology Continued:

• Rational Numbers:

• Exact numbers

• Irrational Numbers:

• Non-exact and exact numbers

• Could contain imaginary values

Terminology Continued:

• Double Roots:

• A root that appears twice in a solution of an algebraic equation.

• Depressed Polynomial:

• A sad polynomial (just kidding)

• Actually: New polynomial after dividing an original one by something.

The Zero Product Rule:

“If (A)(B)(C)=0, then either A = 0, B = 0, or C = 0”

Example:

(x + 8)(x – 1)(2x – 7) = 0

x + 8 = 0 x – 1 = 0 2x – 7 = 0

x = -8 x = 1 x = 7/2= 3.5

You have done this in Algebra by using the….

Quadratic Formula:

For the quadratic function ax2 + bx + c = 0 then:

Complete “Polynomial Equation” worksheets.

If you do not finish them then it is homework.

Quiz: Last ten minutes of class.

• Write at least three questions in the left hand column.

• Summarize your notes by following the “Summary Paragraph Template” at your tables.