Difference between revisions of "Root Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}}
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;Root( <Polynomial> )
; Root[Polynomial]: Yields all roots of the polynomial as intersection points of the function graph and the ''x''‐axis.
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:Yields all roots of the polynomial as intersection points of the function graph and the ''x''‐axis.
; Root[Function, Number a]: Yields one root of the function using the initial value ''a'' for Newton's method.
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:{{example| 1=<code><nowiki>Root(0.1*x^2 - 1.5*x + 5)</nowiki></code> yields ''A = (5, 0)'' and ''B = (10, 0)''.}}
; Root[Function, Number a, Number b]: Yields one root of the function in the interval [''a, b''] (regula falsi).
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;Root( <Function>, <Initial x-Value> )
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:Yields one root of the function using the initial value ''a'' for a numerical iterative method.
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:{{example| 1=<code><nowiki>Root(0.1*x^2 - 1.5*x + 5, 6)</nowiki></code> yields ''A = (5, 0)''.}}
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;Root( <Function>, <Start x-Value>, <End x-Value> )
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:Let ''a'' be the ''Start x-Value'' and ''b'' the ''End x-Value'' . This command yields one root of the function in the interval [''a, b''] using a numerical iterative method.
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:{{example| 1=<code><nowiki>Root(0.1x² - 1.5x + 5, 8, 13)</nowiki></code> yields ''A = (10, 0)''.</div>}}
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==CAS Syntax==
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;Root( <Polynomial> )
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:Yields all roots of the polynomial as intersection points of the function graph and the ''x''‐axis.
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:{{example| 1=<code><nowiki>Root(x^3 - 3 * x^2 - 4 * x + 12)</nowiki></code> yields ''{x = -2, x = 2, x = 3}''.}}
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{{note| 1=<div>In the [[File:Menu view cas.svg|link=|16px]] [[CAS View]], this command is only a special variant of [[Solve Command]].</div>}}

Latest revision as of 08:46, 9 October 2017


Root( <Polynomial> )
Yields all roots of the polynomial as intersection points of the function graph and the x‐axis.
Example: Root(0.1*x^2 - 1.5*x + 5) yields A = (5, 0) and B = (10, 0).


Root( <Function>, <Initial x-Value> )
Yields one root of the function using the initial value a for a numerical iterative method.
Example: Root(0.1*x^2 - 1.5*x + 5, 6) yields A = (5, 0).


Root( <Function>, <Start x-Value>, <End x-Value> )
Let a be the Start x-Value and b the End x-Value . This command yields one root of the function in the interval [a, b] using a numerical iterative method.
Example: Root(0.1x² - 1.5x + 5, 8, 13) yields A = (10, 0).


CAS Syntax

Root( <Polynomial> )
Yields all roots of the polynomial as intersection points of the function graph and the x‐axis.
Example: Root(x^3 - 3 * x^2 - 4 * x + 12) yields {x = -2, x = 2, x = 3}.
Note:
In the Menu view cas.svg CAS View, this command is only a special variant of Solve Command.
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