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Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Moebius <invalid@example.invalid> Newsgroups: sci.math Subject: =?UTF-8?B?UmU6IHjCsis0eCs1PTA=?= Date: Thu, 23 Jan 2025 22:23:45 +0100 Organization: A noiseless patient Spider Lines: 35 Message-ID: <vmuc11$1qjl1$1@dont-email.me> References: <4mVsl7f7IEYIck3oOw7iM3AOjN8@jntp> <vms0ms$196cb$1@dont-email.me> Reply-To: invalid@example.invalid MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 23 Jan 2025 22:23:46 +0100 (CET) Injection-Info: dont-email.me; posting-host="c7f1fc5e7ab30da1f00c5e4683097cd6"; logging-data="1920673"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/hsDjzJ1M1pPA8qxOwDtun" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:ImxEIvmhksEQINIJzLGc3j3MTCo= In-Reply-To: <vms0ms$196cb$1@dont-email.me> Content-Language: de-DE Bytes: 1821 Am 23.01.2025 um 00:58 schrieb sobriquet: > Op 22/01/2025 om 14:48 schreef Richard Hachel: >> x²+4x+5=0 >> >> This equation has no root, and it never will. >> >> We can then find two roots of its mirror curve. >> >> Let x'=-3 and x"=-1 >> >> These are not roots of this curve, but the roots of the imaginary >> mirror curve. >> >> What is this imaginary mirror curve? >> >> It is the curve with equation y=-x²-4x-3 >> >> Let's look for its roots, and we find x'=-3 and x'=-1 >> >> These are the imaginary roots of x²-4x+5. >> >> Or x'=-3(i) and x'=-1(i) >> >> R.H. > > Wolfram Alpha tells us there are two roots: > > https://www.wolframalpha.com/input?i=solve+x%5E2%2B4x%2B5%3D0 Wolfram Alpha must be wrong! :-P .. .. ..