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: − ± 2 − 4 = 2 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.