Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











Root






Mathematica Notation

Traditional Notation









Elementary Functions > Root[polynomialInzk] > Specific values > Specialized values





http://functions.wolfram.com/01.33.03.0002.01









  


  










Input Form





Root[Function[z, Subscript[a, 0] + Subscript[a, 1] z + Subscript[a, 2] z^2], k] == -(Subscript[a, 1]/(2 Subscript[a, 2])) + ((-1)^k/2) Sqrt[(Subscript[a, 1]^2 - 4 Subscript[a, 2] Subscript[a, 0])/ Subscript[a, 2]^2] /; 1 <= k <= 2










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["z", ",", RowBox[List[SubscriptBox["a", "0"], " ", "+", RowBox[List[SubscriptBox["a", "1"], "z"]], "+", RowBox[List[SubscriptBox["a", "2"], SuperscriptBox["z", "2"]]]]]]], "]"]], ",", "k"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[SubscriptBox["a", "1"], RowBox[List["2", " ", SubscriptBox["a", "2"]]]]]], "+", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], "2"], " ", SqrtBox[FractionBox[RowBox[List[SubsuperscriptBox["a", "1", "2"], "-", RowBox[List["4", " ", SubscriptBox["a", "2"], " ", SubscriptBox["a", "0"]]]]], SubsuperscriptBox["a", "2", "2"]]]]]]]]], "/;", RowBox[List["1", "\[LessEqual]", "k", "\[LessEqual]", "2"]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msubsup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> ; </mo> <mrow> <msub> <mi> a </mi> <mn> 0 </mn> </msub> <mo> + </mo> <mtext> </mtext> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> k </mi> </msup> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mtext> </mtext> <msqrt> <mfrac> <mrow> <msubsup> <mi> a </mi> <mn> 1 </mn> <mn> 2 </mn> </msubsup> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 0 </mn> </msub> </mrow> </mrow> <msubsup> <mi> a </mi> <mn> 2 </mn> <mn> 2 </mn> </msubsup> </mfrac> </msqrt> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mn> 1 </mn> <mo> &#8804; </mo> <mi> k </mi> <mo> &#8804; </mo> <mn> 2 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> CompoundExpression </ci> <ci> z </ci> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> k </ci> <cn type='integer'> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Root", "[", RowBox[List[RowBox[List["Function", "[", RowBox[List["z_", ",", RowBox[List[SubscriptBox["a_", "0"], "+", RowBox[List[SubscriptBox["a_", "1"], " ", "z_"]], "+", RowBox[List[SubscriptBox["a_", "2"], " ", SuperscriptBox["z_", "2"]]]]]]], "]"]], ",", "k_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[SubscriptBox["aa", "1"], RowBox[List["2", " ", SubscriptBox["aa", "2"]]]]]], "+", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SqrtBox[FractionBox[RowBox[List[SubsuperscriptBox["aa", "1", "2"], "-", RowBox[List["4", " ", SubscriptBox["aa", "2"], " ", SubscriptBox["aa", "0"]]]]], SubsuperscriptBox["aa", "2", "2"]]]]]]], "/;", RowBox[List["1", "\[LessEqual]", "k", "\[LessEqual]", "2"]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2001-10-29