2.6 Theorems About Roots of Polynomials PG 98. Objectives Use the Rational Root Theorem to list all possible roots of a polynomial Test possible roots.

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Presentation transcript:

2.6 Theorems About Roots of Polynomials PG 98

Objectives Use the Rational Root Theorem to list all possible roots of a polynomial Test possible roots to find actual roots Use Conjugate Root Theorem to find pairs of roots

Rational Root Theorem

If a problem asks for “all possible rational roots” then you list all the p/q’s If a problem asks for “rational roots” then: 1.Use your graphing calculator to find 1 root (x= some number like 3). 2.Use that root for synthetic division (plug 3 into the box) to break down the function. 3.Repeat steps 1 and 2 if still have a cubic or higher degree polynomial, until get down to a quadratic polynomial. 4.Now factor or use the quadratic formula to break down to find all the factors and remaining roots.

Rational Root Theorem

p. 99 Got It? and Practice 1,2

Rational Root Theorem

Conjugate Root Theorem

p. 100 Got It? and Practice 5,6

Problem 4 Got it: Pg 101 Replace with the below example

HW 2.6 Pg # 11-15, 17a, 17b, 19, 20, 24, 25