TI-BASIC:Quadratic Formula - Revision history

Maintenance script: Automated internal link correction

2016-02-24T23:22:36Z

Automated internal link correction

← Older revision		Revision as of 23:22, 24 February 2016
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	-2C/(B+{-1,1}√(B²+4ACi²		-2C/(B+{-1,1}√(B²+4ACi²

	For optimization purposes, an alternate form of the quadratic formula is used (see below for the formulas). The {-1,1} list is used to replace the ± symbol -- lists can be used just as well as numbers in expressions, making the result a list as well. By using ''i''² in the expression in place of subtraction, the routine avoids having to activate [[TI-BASIC:~~A+bi~~\|A+bi]] mode to allow complex roots.		For optimization purposes, an alternate form of the quadratic formula is used (see below for the formulas). The {-1,1} list is used to replace the ± symbol -- lists can be used just as well as numbers in expressions, making the result a list as well. By using ''i''² in the expression in place of subtraction, the routine avoids having to activate [[TI-BASIC:A_Bi\|A+bi]] mode to allow complex roots.

	The output is a complex list in [[TI-BASIC:Ans\|Ans]] of the two roots. If there is only one root, it will be returned twice. If both roots are real, they will still be returned correctly, but stored internally as complex numbers -- so use the [[TI-BASIC:Real_Func\|real(]] command on them if you want to pass them to commands that don't accept complex arguments.		The output is a complex list in [[TI-BASIC:Ans\|Ans]] of the two roots. If there is only one root, it will be returned twice. If both roots are real, they will still be returned correctly, but stored internally as complex numbers -- so use the [[TI-BASIC:Real_Func\|real(]] command on them if you want to pass them to commands that don't accept complex arguments.

Maintenance script: Automated superscript correction

2016-02-24T22:25:43Z

Automated superscript correction

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	\|picture=		\|picture=
	\|summary=Solves for the complex roots of a quadratic equation.		\|summary=Solves for the complex roots of a quadratic equation.
	\|input=''A, B, C'' - the constants in Ax^^2^^+Bx+C=0		\|input=''A, B, C'' - the constants in Ax<sup>2</sup>+Bx+C=0
	\|output=''Ans'' - a 2-element list of the two roots (or the one repeated root)		\|output=''Ans'' - a 2-element list of the two roots (or the one repeated root)
	\|variable=A, B, C		\|variable=A, B, C

Maintenance script: Automated @@ correction

2016-02-24T22:12:53Z

Automated @@ correction

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	{{Template:TI-BASIC:Routine		{{Template:TI-BASIC:Routine
	\|picture=@@		\|picture=
	\|summary=Solves for the complex roots of a quadratic equation.		\|summary=Solves for the complex roots of a quadratic equation.
	\|input=''A, B, C'' - the constants in Ax^^2^^+Bx+C=0		\|input=''A, B, C'' - the constants in Ax^^2^^+Bx+C=0
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	\|compatibility=TI-83/84/+/SE		\|compatibility=TI-83/84/+/SE
	\|author=thornahawk		\|author=thornahawk
	\|authors=@@		\|authors=
	\|url=http://www.unitedti.org/index.php?showtopic=7392&view=findpost&p=116156 United TI		\|url=http://www.unitedti.org/index.php?showtopic=7392&view=findpost&p=116156 United TI
	\|download=[file quadraticformula.zip]		\|download=[file quadraticformula.zip]

KermMartian at 19:25, 24 February 2016

2016-02-24T19:25:41Z

← Older revision		Revision as of 19:25, 24 February 2016
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	The ordinary quadratic formula, and its alternate form are used:		The ordinary quadratic formula, and its alternate form are used:

	~~[[TI-BASIC:Math\|Math]]~~		<math>
	\begin{align}		\begin{align}
	\mathrm{For} \hspace{5pt} ax^2+bx+c = 0, \\ \\		\mathrm{For} \hspace{5pt} ax^2+bx+c = 0, \\ \\
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	x = \frac{2c}{-b\pm\sqrt{b^2-4ac}}		x = \frac{2c}{-b\pm\sqrt{b^2-4ac}}
	\end{align}		\end{align}
	~~[[TI-BASIC:~~/math~~\|/math]]~~[[Category:TI-BASIC]]		</math>
			[[Category:TI-BASIC]]
	[[Category:TIBD]]		[[Category:TIBD]]

Maintenance script: Initial automated import

2016-02-24T18:38:22Z

Initial automated import

New page

{{Template:TI-BASIC:Routine
|picture=@@
|summary=Solves for the complex roots of a quadratic equation.
|input=''A, B, C'' - the constants in Ax^^2^^+Bx+C=0
|output=''Ans'' - a 2-element list of the two roots (or the one repeated root)
|variable=A, B, C
|compatibility=TI-83/84/+/SE
|author=thornahawk
|authors=@@
|url=http://www.unitedti.org/index.php?showtopic=7392&view=findpost&p=116156 United TI
|download=[file quadraticformula.zip]
}}

-2C/(B+{-1,1}√(B²+4ACi²

For optimization purposes, an alternate form of the quadratic formula is used (see below for the formulas). The {-1,1} list is used to replace the ± symbol -- lists can be used just as well as numbers in expressions, making the result a list as well. By using ''i''² in the expression in place of subtraction, the routine avoids having to activate [[TI-BASIC:A+bi|A+bi]] mode to allow complex roots.

The output is a complex list in [[TI-BASIC:Ans|Ans]] of the two roots. If there is only one root, it will be returned twice. If both roots are real, they will still be returned correctly, but stored internally as complex numbers -- so use the [[TI-BASIC:Real_Func|real(]] command on them if you want to pass them to commands that don't accept complex arguments.

= Advanced =

The ordinary formula above can give poor results if B is much larger than A and/or C. In that case, an alternate routine can be used:

√(B²+4ACi²
If 0>real(Ansconj(B
-Ans
-.5(B+Ans
{Ans/A,C/Ans

= Formulas =

The ordinary quadratic formula, and its alternate form are used:

[[TI-BASIC:Math|Math]]
\begin{align}
\mathrm{For} \hspace{5pt} ax^2+bx+c = 0, \\ \\
x = \frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\
x = \frac{2c}{-b\pm\sqrt{b^2-4ac}}
\end{align}
[[TI-BASIC:/math|/math]][[Category:TI-BASIC]]
[[Category:TIBD]]