Activity 2 a 10Ot OI Imuluplic a) Show that 4/3 is a root of P(x) = 27x³ – 108x² + 144x – 64. %3D b) Find all the roots of P(x). What is the multiplicity of the root 4/3? Learning Point 2 Find the rational roots of a polynomial. Concepts 4 -5 ynomial nd regardless of üts natn relless of

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 91E
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5)2X2 – x- 15) = (x – 3)(x- 3)(2x+ 5).
The other roots are 3 and -2.5.
In the previous example, 3 is a repeated root. More specifically, 3 is a root of
multiplicity 2. If a root is repeated m times, we call it a root of multiplicity m.
Activity 2
a) Show that 4/3 is a root of P(x) = 27x³ – 108x² + 144x – 64.
%3D
b) Find all the roots of P(x). What is the multiplicity of the root 4/3?
Learning Point 2
Find the rational roots of a polynomial.
Concepts 4 -5
Co
a) E
b) Fa
Finding the rational roots of a polynomial
A polynomial of degree 1 has one root which can be found regardless oaf
A polynomial of degree 2 has two roots which can also be found regardie
There are ways to find the roots of of degree 3 or 4 but we wil nor
here. Instead, we will only focus on
nature.
polynomials whose roots, exc
pomial has a pabkonl
Transcribed Image Text:リー 5)2X2 – x- 15) = (x – 3)(x- 3)(2x+ 5). The other roots are 3 and -2.5. In the previous example, 3 is a repeated root. More specifically, 3 is a root of multiplicity 2. If a root is repeated m times, we call it a root of multiplicity m. Activity 2 a) Show that 4/3 is a root of P(x) = 27x³ – 108x² + 144x – 64. %3D b) Find all the roots of P(x). What is the multiplicity of the root 4/3? Learning Point 2 Find the rational roots of a polynomial. Concepts 4 -5 Co a) E b) Fa Finding the rational roots of a polynomial A polynomial of degree 1 has one root which can be found regardless oaf A polynomial of degree 2 has two roots which can also be found regardie There are ways to find the roots of of degree 3 or 4 but we wil nor here. Instead, we will only focus on nature. polynomials whose roots, exc pomial has a pabkonl
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