19) Using Rational Root Theorem and Descartes' Rule of signs. Types of Positive Negative Imaginary Roots Roots (Pairs) 3 Find all roots of f(x)=x³ - 2x² - 5x + 6. Roots What are the factors of the constant term? p= ± Possibility 1: Factors of the teading Coefficient term? Possibility 2: q= ± Rational Roots All possible rational roots + (Remainder) Descartes' Rule Find sign changes. Make reduced Poly x³ - 2x²-5x + 6 Positive = (-x)³ -2(-x)² - 5(-x) + 6 Negative = Factor or Solve Roots X =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 17E
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19) Using Rational Root Theorem and Descartes' Rule of signs.
Types of Positive Negative Imaginary
3
Find all roots of f(x)=X³ - 2x² - 5x + 6.
Roots
What are the factors of the constant term?
Roots
Roots
(Pairs)
p= ±
Possibility 1:
Factors of the Leading Coefficient term?
Possibility 2:
q= ±
All possible rational roots
+
(Remainder)
Descartes' Rule Find sign changes.
x³ - 2x² -5x + 6
Positive =
(-x)³-2(-x)²-5(-x) + 6
Negative:
=
er notes
%
5
Rational Roots+
V6
9
y
Make reduced Poly
Factor or Solve
Roots x =
&
7
B
Transcribed Image Text:19) Using Rational Root Theorem and Descartes' Rule of signs. Types of Positive Negative Imaginary 3 Find all roots of f(x)=X³ - 2x² - 5x + 6. Roots What are the factors of the constant term? Roots Roots (Pairs) p= ± Possibility 1: Factors of the Leading Coefficient term? Possibility 2: q= ± All possible rational roots + (Remainder) Descartes' Rule Find sign changes. x³ - 2x² -5x + 6 Positive = (-x)³-2(-x)²-5(-x) + 6 Negative: = er notes % 5 Rational Roots+ V6 9 y Make reduced Poly Factor or Solve Roots x = & 7 B
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