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+--- Thread: Cubic / quartic exact solutions (/thread-3164.html)
Cubic / quartic exact solutions - LCieParagon - 02-21-2015 04:42 PM
Hello everyone.
I was just curious if an App exists to find exact values for a cubic and quartic polynomial rather than decimal approximations. I know Maple can provide exact answers, but I've yet to see a calculator do this.
The solutions are right here:
https://suhaimiramly.files.wordpress.com/2010/04/quartic.jpg
https://31.media.tumblr.com/tumblr_mcmirdHLhE1rvnfhg.png
Thanks.
RE: Cubic / quartic exact solutions - Dieter - 02-21-2015 05:09 PM
(02-21-2015 04:42 PM)LCieParagon Wrote: I was just curious if an App exists to find exact values for a cubic and quartic polynomial rather than decimal approximations. I know Maple can provide exact answers, but I've yet to see a calculator do this.
You asked the same question in the general forum. As already mentioned there, solving cubic equations is rather trivial and it's done with calculators since the Seventies.
(02-21-2015 04:42 PM)LCieParagon Wrote: The solutions are right here:
...
https://31.media.tumblr.com/tumblr_mcmirdHLhE1rvnfhg.png
As far as I can tell this is only the solution for a cubic function with one real and two complex roots. The general solution (including three real roots) can be found e.g. in the link I provided in the other thread. As already mentioned, there are several methods of solving cubic equations.
Since this is no Prime-specific topic I'd suggest continuing the discussion in the general forum.
Dieter
RE: Cubic / quartic exact solutions - LCieParagon - 02-21-2015 06:01 PM
(02-21-2015 05:09 PM)Dieter Wrote:(02-21-2015 04:42 PM)LCieParagon Wrote: I was just curious if an App exists to find exact values for a cubic and quartic polynomial rather than decimal approximations. I know Maple can provide exact answers, but I've yet to see a calculator do this.
You asked the same question in the general forum. As already mentioned there, solving cubic equations is rather trivial and it's done with calculators since the Seventies.
(02-21-2015 04:42 PM)LCieParagon Wrote: The solutions are right here:
...
https://31.media.tumblr.com/tumblr_mcmirdHLhE1rvnfhg.png
As far as I can tell this is only the solution for a cubic function with one real and two complex roots. The general solution (including three real roots) can be found e.g. in the link I provided in the other thread. As already mentioned, there are several methods of solving cubic equations.
Since this is no Prime-specific topic I'd suggest continuing the discussion in the general forum.
Dieter
It's meant for a Prime calculator. I'm aware of how to calculate solutions. I'm a differential equations teacher. I would like an exact solution rather than an approximation.
I only own the Prime (and other TI calculators). None give me an answer in root form.
RE: Cubic / quartic exact solutions - LCieParagon - 02-21-2015 06:02 PM
(02-21-2015 05:09 PM)Dieter Wrote:(02-21-2015 04:42 PM)LCieParagon Wrote: I was just curious if an App exists to find exact values for a cubic and quartic polynomial rather than decimal approximations. I know Maple can provide exact answers, but I've yet to see a calculator do this.
You asked the same question in the general forum. As already mentioned there, solving cubic equations is rather trivial and it's done with calculators since the Seventies.
(02-21-2015 04:42 PM)LCieParagon Wrote: The solutions are right here:
...
https://31.media.tumblr.com/tumblr_mcmirdHLhE1rvnfhg.png
As far as I can tell this is only the solution for a cubic function with one real and two complex roots. The general solution (including three real roots) can be found e.g. in the link I provided in the other thread. As already mentioned, there are several methods of solving cubic equations.
Since this is no Prime-specific topic I'd suggest continuing the discussion in the general forum.
Dieter
Additionally, you have stated that the solutions only provide one real and two complex roots. That's false since the portion under the radical may be negative and multiplying i by i will get you a real solution.