MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C8196E.5674C7D0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C8196E.5674C7D0 Content-Location: file:///C:/B141D692/PolynomialFunctionsUnitFourASRR.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Determine the Solution Set of a Polynomial Function – Unit (4)=

 Determine the Solution Set for a Polynomial Function with Rational Roots

Students should be able to sketch from knowledge of Polynomials the appearance of a 4th Degree Solution Set.<= /b>

***********= *********************************

 

Given: F(X) =3D 2X3 + 3X2 –11X  – 6              Use Synthetic Division to investigate = possible roots.

 

            [+ 1]    +2        +3        -11       -6        &= nbsp;            [– 1]     +2        +3        -11       -6

           &nb= sp;            0        &= nbsp; +2        +5        -6        &= nbsp;           &nbs= p;            0        &= nbsp; -2         = -1         = +12

           &nb= sp;            +2        +5        -6         = -12 Point        &= nbsp;            +2        +1        -12       +6 Point

 

            [+ 2]    +2        +3        -11       -6        &= nbsp;            [– 2]     +2        +3        -11       -6

           &nb= sp;              0&= nbsp;       +4        +14     +6        &= nbsp;           &nbs= p;               0       -4         = +2        +18

           &nb= sp;            +2        +7        +3        0  Root=         &= nbsp;           &nbs= p;   +2        -1         = -9         = +12

 

Therefore X =3D +2<= span style=3D'mso-spacerun:yes'>  is a Root and  +2X2  +7X  +3  is the Depressed Equation  and contains the remaining two roo= ts.

&nbs= p;

+2X2=   +7X  +3  =3D  ( 2X  + 1 ) ( X  + 3)  or  X =3D -1/2   and X= =3D -3       Now generate more points.

 

 

            [+ 3]    +2        +3        -11       -6

           &nb= sp;            0        &= nbsp; +6        +27      +48     

           &nb= sp;            +2        +9        +16      +42     

 

            [+ 4]    +2        +3        -11       -6        &= nbsp;            [– 4]     +2        +3        -11       -6

           &nb= sp;            0        &= nbsp; +8        +44      +132        &= nbsp;           &nbs= p;       0        &= nbsp; -8         = +20      -36

           &nb= sp;            +2        +11      +33      + 126        &= nbsp;           &nbs= p;      +2        -5         = +9        -42

           &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;            = ;            &n= bsp;        

 

 

 

X

+2

-3

-1/2

 

+3

+4

-4

Y

0

0

0

 

+42

+126

-42

 

From determination of the intercepts (r= oots) and other relative points the Solution Set appears as seen.

&n= bsp;

Tom Love=         =             &nb= sp;       Malone College        =             &nb= sp;     Fall 2007

&n= bsp;

 

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Tom Love=         =             &nb= sp;            =        Malone College        =             &nb= sp;               =   Fall 2003

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