**Topic: **
| Roots of Polynomial Equations |

**Content: **
| Rational Root Theorem, synthetic division, conjugates, Irrational Root Theorem, Imaginary Root Theorem, quadratic formula |

**Goals: **
| 1) Show students the rational root theorem and how and when to use it.
2) Remind students of the term conjugates
3) Show students the irrational and imaginary root theorems and their usefulness |

**Objectives:**
| 1) Students will learn the Rational Root Theorem and how to use it
2) Students will practice working with the Rational Root Theorem
3) Students will learn what the Irrational and Imaginary Root Theorems mean
4) Students will practice finding roots given known roots |

**Materials:**
| overhead, overhead markers, transparencies, whiteboard, whiteboard markers, overhead calculator |

**Introduction:**
| Teacher reminds students of the methods used so far to find roots (zeros, solutions) of polynomials. These methods include factoring, sum/difference of cubes, substitution, long/synthetic division, and the quadratic formula. |

**Development:**
| Teacher states the Rational Root Theorem and explains its meaning in simpler terms. Teacher then gives examples of how to find the rational roots of a polynomial. Next, the teacher extends the knowledge by showing the students how to find all of the zeros using the Rational Root Theorem. The students are then introduced to the Irrational and Imaginary Root Theorems and their usefulness in finding roots. |

**Practice:**
| Ex.1: Find the rational roots of (x^3)-4(x^2)-2x+8
Ex.2: Find all roots of 3(x^3)+(x^2)-x+1=0
Ex.3: Given 2-(5)^1/2 and (7)^1/2 as roots of a polynomial, find 2 more roots
Ex.4: Given 2+9i and 7i as roots of a polynomial, find 2 more. |

**Accommodations:**
| different colors, technology, verbal and visual instructions and directions |

**Checking For Understanding:**
| Periodically throughout the lecture, teacher pauses to check for students' understanding. Teacher has students list out possible roots. |

**Closure:**
| Teacher ends the lecture by giving the homework assignment and reminding students to show their work. |