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Find all roots of a high-order equation
The math behide this solution is quite simple: if a polynomial equation f(x)=0 has roots, let's say x1,x2,……xn,then f(x) can be converted to another format as (x-x1)*(x-x2)*(x-x3)*…...*(x-xn) = 0 So what we do here is use goal-seek to find it's first root(x1) then use f(x) / (x-x1) as a new equation, easy to say the new one is (x-x2)*(x-x3)*…...*(x-xn) = 0 repeat the procedure above,we can get all the roots one by one. +-------------------------------------------------------------------+ |Filename: Find all the roots of High-Order Polynomial Equation by Dragon.Pan.zip| |Download: http://www.excelforum.com/attachment.php?postid=3956 | +-------------------------------------------------------------------+ -- Pan ------------------------------------------------------------------------ Pan's Profile: http://www.excelforum.com/member.php...o&userid=28144 View this thread: http://www.excelforum.com/showthread...hreadid=480008 |
#2
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Find all roots of a high-order equation
I know know if excel is the best way to go here.... There's a program called Maple that would be of use to you... www.maplesoft.com However, if there is an excel solution, I'm sure someone on here can figure it out. - Search "Pan" wrote: The math behide this solution is quite simple: if a polynomial equation f(x)=0 has roots, let's say x1,x2,€¦€¦xn,then f(x) can be converted to another format as (x-x1)*(x-x2)*(x-x3)*€¦...*(x-xn) = 0 So what we do here is use goal-seek to find it's first root(x1) then use f(x) / (x-x1) as a new equation, easy to say the new one is (x-x2)*(x-x3)*€¦...*(x-xn) = 0 repeat the procedure above,we can get all the roots one by one. +-------------------------------------------------------------------+ |Filename: Find all the roots of High-Order Polynomial Equation by Dragon.Pan.zip| |Download: http://www.excelforum.com/attachment.php?postid=3956 | +-------------------------------------------------------------------+ -- Pan ------------------------------------------------------------------------ Pan's Profile: http://www.excelforum.com/member.php...o&userid=28144 View this thread: http://www.excelforum.com/showthread...hreadid=480008 |
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