Numerically, it's much more precise to run iteratives methods to find root approximations. If you are showing exact formula for 3rd or 4th order equations to your students, you should really emphasize that they should in fact never be used. RE: Cubic and Quartic Formulae - parisse - 08-06-2015 12:01 PM The things people do for their calculators (obviating the existence of computers and the ephemeral quality of life) never cease to amaze me. (08-06-2015 09:07 AM)Gerald H Wrote: But note this:Īnd now I have to take that remark back. RE: Cubic and Quartic Formulae - Manolo Sobrino - 08-06-2015 09:20 AM RE: Cubic and Quartic Formulae - Gerald H - 08-06-2015 09:07 AM Taking into account the constraints of the machine it was designed for and its intended use, all of this makes sense to me. TI have actually given details on the nifty algorithm they used in their numerical polynomial root finder, which appeared first on the TI 85: I guess you won't be using calculators to introduce Galois theory. The interesting part about them is that they do exist and they are algebraic expressions, yet the quintic doesn't have one of this kind (Abel-Ruffini theorem). There are quite a few much better methods. That's the same reason why closed form eigenvalues are either trivial or you don't really want to see them.Īnd then, in the numerical world people don't use (or shouldn't be using) those expressions as they are numerically unstable. That's not very useful, besides it would only look nice (not really) for integer or rational coefficients. You want 3 or 4 several line expressions with nested radicals as answers on a calculator screen. RE: Cubic and Quartic Formulae - Manolo Sobrino - 08-06-2015 09:01 AM I'm sure the ability is there to put this feature in. I mean when computing (-1)^(1/3), you get the principal complex root as opposed to -1. I never understood why calculators with this capability gave approximate answers as opposed to exact. However, there is obviously an exact solution given that it is a cubic polynomial. You receive a decimal value approximately -0.68. Quite clearly you can see what I mean when I type: solve(x^3+x+1=0,x) RE: Cubic and Quartic Formulae - LCieParagon - 08-06-2015 05:42 AM I'm a math teacher and I would like to show my students exact answers of these polynomials rather than just decimal approximations. Only linear (trivial) and quadratic equations provide exact answers for all values of a, b, c. I wish the HP Prime and TI calculators provided exact solutions. These formulae have been known since the 1500s. I'm well aware that the calculator can solve them, but they provide decimal, approximate answers. I am just wondering if anyone has a program / application to find the exact roots of cubic and quartic polynomials. +- Thread: Cubic and Quartic Formulae ( /thread-4487.html)Ĭubic and Quartic Formulae - LCieParagon - 08-06-2015 05:35 AM +- Forum: HP Calculators (and very old HP Computers) ( /forum-3.html) Cubic and Quartic Formulae - Printable Version
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