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:
How do find all zeros in a polynomial equation?
Notes:
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
Notes:
Terminology Continued:
• Rational Numbers:
– Exact numbers
• Irrational Numbers:
– Non-exact and exact numbers
– Could contain imaginary values
Notes:
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=0
x–1=0
2x – 7 = 0
x = -8
x=1
x = 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:
−𝑏 ± 𝑏 2 − 4𝑎𝑐
𝑥=
2𝑎
Your Assignment:
Complete “Polynomial Equation” worksheets.
If you do not finish them then it is homework.
Quiz: Last ten minutes of class.
Quiz Time!
Exit Ticket:
1. Write at least three questions in the left hand
column.
2. Summarize your notes by following the
“Summary Paragraph Template” at your
tables.