Quintic EquationsDate: 1/27/96 at 11:36:21 From: Anonymous Subject: definition I'm taking an Internet course and it's being held in a math lab at UIC in Chicago. On the wall is a poster called "Solving Quintic". I tried looking up the word Quintic in the Webster's on-line dictionary and found nothing. What does Quintic mean? Is it a math term or a product name? I'm just an elementary school teacher and am curious. Date: 1/27/96 at 12:26:29 From: Doctor Sarah Subject: Re: definition Hello there - You're on the right track using the Internet to look for the quintic. If you have an online dictionary you'll probably also have access to a Web browser, right? You can try using a searcher like Alta Vista at http://altavista.digital.com/ to search for 'quintic'. Here's one of the pages it finds: STEPS TO THE QUINTIC http://www.wri.com/posters/quintic/main.html The page takes you through the quadratic, cubic, and quartic equations on the way to the quintic. You know what the quadratic equation looks like, right? ax^2 + bx + c = d (where a, b, c, and d are real numbers and a does not equal zero) The quintic looks like this: ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0, x I'll let you look up the answer (found using Mathematica) on the Web page. Here's some of what it says: "Root objects are an implicit way to represent the solution. They can be differentiated and expanded out in series, and with approximate numerical values for the coefficients, they immediately yield a numerical solution. Of course, we can solve a quintic with numerical coefficients immediately by using the built-in Mathematica function NSolve. "Ruffini (1799) and Abel (1826) proved that it is not possible to give an explicit solution for the general quintic equation with symbolic coefficients in terms of square roots, cube roots, and so on. Is there an explicit solution to the quintic with symbolic coefficients? Yes! In the late 1800s, several mathematicians constructed such solutions. However, it was necessary to go beyond the extraction of roots and to use elliptic and hypergeometric functions. Mathematica can handle these higher mathematical functions in the same way as ordinary trigonometric or exponential functions. Combined with Mathematica's algebraic capabilities, this makes it possible to implement various symbolic solutions to the quintic." There's a lot more. Enjoy! -Doctor Sarah, The Math Forum |
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