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Pre-Calculus

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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.

Finding Solutions:

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 = 0x – 1 = 02x – 7 = 0

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

Finding Irrational Solutions:

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.