please help with polynomials (1 Viewer)

mOusaa · Mar 29, 2010

hey guys I'm struggling with these two questions

Find all solutions of the polynomial p(x)=<meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 12"><meta name="Originator" content="Microsoft Word 12"><link rel="File-List" href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml"><link rel="themeData" href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx"><link rel="colorSchemeMapping" href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml"><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w

unctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w

oNotPromoteQF/> <w:LidThemeOther>EN-AU</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w

ontGrowAutofit/> <w:SplitPgBreakAndParaMark/> <w

ontVertAlignCellWithSp/> <w

ontBreakConstrainedForcedTables/> <w

ontVertAlignInTxbx/> <w:Word11KerningPairs/> <w:CachedColBalance/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--"/> <m:smallFrac m:val="off"/> <m:dispDef/> <m:lMargin m:val="0"/> <m:rMargin m:val="0"/> <m:defJc m:val="centerGroup"/> <m:wrapIndent m:val="1440"/> <m:intLim m:val="subSup"/> <m:naryLim m:val="undOvr"/> </m:mathPr></w:WordDocument> </xml><![endif]--><style>  </style>[FONT=&quot]x^4 - 6x^3 + 15x^2 - 18x + 10 given that 1-i is a root.

Find all roots of [/FONT]<meta http-equiv="Content-Type" content="text/html; charset=utf-8"><meta name="ProgId" content="Word.Document"><meta name="Generator" content="Microsoft Word 12"><meta name="Originator" content="Microsoft Word 12"><link rel="File-List" href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml"><link rel="themeData" href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx"><link rel="colorSchemeMapping" href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml"><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:TrackMoves/> <w:TrackFormatting/> <w

unctuationKerning/> <w:ValidateAgainstSchemas/> <w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid> <w:IgnoreMixedContent>false</w:IgnoreMixedContent> <w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText> <w

oNotPromoteQF/> <w:LidThemeOther>EN-AU</w:LidThemeOther> <w:LidThemeAsian>X-NONE</w:LidThemeAsian> <w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript> <w:Compatibility> <w:BreakWrappedTables/> <w:SnapToGridInCell/> <w:WrapTextWithPunct/> <w:UseAsianBreakRules/> <w

ontGrowAutofit/> <w:SplitPgBreakAndParaMark/> <w

ontVertAlignCellWithSp/> <w

ontBreakConstrainedForcedTables/> <w

ontVertAlignInTxbx/> <w:Word11KerningPairs/> <w:CachedColBalance/> </w:Compatibility> <w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel> <m:mathPr> <m:mathFont m:val="Cambria Math"/> <m:brkBin m:val="before"/> <m:brkBinSub m:val="--"/> <m:smallFrac m:val="off"/> <m:dispDef/> <m:lMargin m:val="0"/> <m:rMargin m:val="0"/> <m:defJc m:val="centerGroup"/> <m:wrapIndent m:val="1440"/> <m:intLim m:val="subSup"/> <m:naryLim m:val="undOvr"/> </m:mathPr></w:WordDocument> </xml><![endif]--><style>  </style>[FONT=&quot]lzl^2 + z̄ +2z = sqrt(2i) by writing z as a+ib

any help would be greatly appreciated
[/FONT]

mOusaa · Mar 29, 2010

anyone?

tommykins · Mar 29, 2010

show us your working then we'll help you.

mOusaa · Mar 29, 2010

i don't know what to do with all the i's, i could do it if it had no i's but i don't even know what i have to do to the i's

captainvagina · Mar 29, 2010

if 1-i is a root then 1+i is also a root
[x-(1-i)][x-(1+i)]
multiply out and u will get a quadratic which you can use to divide into the original polynomial

captainvagina · Mar 29, 2010

mOusaa said:
hey guys I'm struggling with these two questions

Find all solutions of the polynomial p(x)=<META name=ProgId content=Word.Document><META name=Generator content="Microsoft Word 12"><META name=Originator content="Microsoft Word 12"><LINK rel=File-List href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml"><LINK rel=themeData href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx"><LINK rel=colorSchemeMapping href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml"><STYLE>  </STYLE>[FONT=&quot]x^4 - 6x^3 + 15x^2 - 18x + 10 given that 1-i is a root.[/FONT]

[FONT=&quot]Find all roots of [/FONT]<META name=ProgId content=Word.Document><META name=Generator content="Microsoft Word 12"><META name=Originator content="Microsoft Word 12"><LINK rel=File-List href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml"><LINK rel=themeData href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx"><LINK rel=colorSchemeMapping href="file:///C:%5CUsers%5CMOUSSA%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml"><STYLE>  </STYLE>[FONT=&quot]lzl^2 + z̄ +2z = sqrt(2i) by writing z as a+ib[/FONT]

[FONT=&quot]any help would be greatly appreciated[/FONT]

for the second part just sub in z=a+ib
lzl^2 + z̄ +2z
(sqrt(a^2+b^2))^2 + i(a+ib) + 2(a+ib)
expand this out then equate real and imaginary parts

Carrotsticks · Mar 30, 2010

captainvagina said:
if 1-i is a root then 1+i is also a root

You can't just say that. You need to explain that ONLY because all the coeffs are real, then 1+i is also a root.

captainvagina · Mar 30, 2010

Carrotsticks said:
You can't just say that. You need to explain that ONLY because all the coeffs are real, then 1+i is also a root.

i know i just cbf typing all that........im sure he already knows that polynomials with real coefficients have conjugate complex root pairs

please help with polynomials (1 Viewer)

mOusaa

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mOusaa

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tommykins

i am number -e^i*pi

mOusaa

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captainvagina

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Carrotsticks

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