tag:blogger.com,1999:blog-9004452969563620551.post7138920810104993412..comments2024-03-03T08:58:16.415+05:30Comments on Paramanand's Math Notes: Abel and the Insolvability of the Quintic: Part 1Unknownnoreply@blogger.comBlogger5125tag:blogger.com,1999:blog-9004452969563620551.post-85073085921662989122019-11-03T08:01:50.475+05:302019-11-03T08:01:50.475+05:30> if the root of an equation could be expressed...> if the root of an equation could be expressed as a radical expression in the coefficients<br /><br />> in case of a quadratic equation <br />x^2+ax+b=0 the radical expression <br />√(a^2−4b) is either x1−x2 or x2−x1<br /><br />But √(a^2−4b) isn't a root. -a+(√(a^2−4b))/2 are the roots.<br /><br />Something seems imprecisely stated here, and I can't see how to fix it.<br /><br />Did you mean something like "if the root of an equation could be expressed as a rational expression in [cofficients and [radical expression in the coefficients]]..."<br /><br /><br /><br /><br />Michael Rogerhttps://www.blogger.com/profile/08729150476888743293noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-87890313248817188152019-11-03T07:39:01.034+05:302019-11-03T07:39:01.034+05:30> \mathbb{C}(s_{1}, s_{2}, \ldots, x_{n}) repre...> \mathbb{C}(s_{1}, s_{2}, \ldots, x_{n}) represents the field of symmetric rational expressions<br /><br />You meant \mathbb{C}(s_{1}, s_{2}, \ldots, s_{n})<br />, yes?<br /><br /><br />Expressions over an individual x_i cannot be symmetric over the set of x_i.Michael Rogerhttps://www.blogger.com/profile/08729150476888743293noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-29863449724591178862019-01-05T13:47:05.461+05:302019-01-05T13:47:05.461+05:30Even the general solution to quadratic equation wa...Even the general solution to quadratic equation was incorrect,<br /><br />Kindly, read some issues here, it is too elementary to get them in few minutes, for sure<br />https://www.quora.com/Does-sqrt-3-2-really-exist-on-the-real-number-line-or-does-it-exist-only-in-our-minds/answer/Bassam-Karzeddin-1<br /><br />B.Karzeddin<br />Bassam Karzeddinhttps://www.blogger.com/profile/14045449865510210365noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-82662695614242837892019-01-05T13:46:08.302+05:302019-01-05T13:46:08.302+05:30Even the general solution to quadratic equation wa...Even the general solution to quadratic equation was incorrect,<br /><br />Kindly, read some issues here, it is too elementary to get them in few minutes, for sure<br />https://www.quora.com/Does-sqrt-3-2-really-exist-on-the-real-number-line-or-does-it-exist-only-in-our-minds/answer/Bassam-Karzeddin-1<br /><br />B.Karzeddin<br />Bassam Karzeddinhttps://www.blogger.com/profile/14045449865510210365noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-12559647512044120412017-04-03T10:26:30.408+05:302017-04-03T10:26:30.408+05:30Hi,
I'm not nearly good enough to understand ...Hi,<br /><br />I'm not nearly good enough to understand the proof, but I found the derivation of the cubic formula really interesting. I've never found any other site that provides the reasons behind how the transformation to a depressed cubic works (I understood the Vieta's but didn't make the connection.) Thanks so much!.Anonymousnoreply@blogger.com