Talk:Quadratic formula

Wiki Education Foundation-supported course assignment

This article was the subject of a Wiki Education Foundation-supported course assignment, between 7 September 2020 and 18 December 2020. Further details are available on the course page. Student editor(s): AH-2031.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 07:34, 17 January 2022 (UTC)

Shreedharayacharya's formula

In India, quadratic formula is popularly known as Shreedharacharya's formula (or Sridharacharya's formula) as it was first given by an ancient Indian mathematician Shreedharacharya (or Sridharacharya) or Sridhara around 1025 A.D. Huzaifa abedeen (talk) 14:23, 4 November 2020 (UTC)

Citation needed

Does there really need to be a citation at the end of the subsection "Method 3"?  AltoStev ^Talk 12:43, 27 October 2021 (UTC)

Not really. But I did some cleaning up, removing reduncancies. There was nothing in the first part of subsection "Method 2" and in subsection "Method 3" that wasn't already there. - DVdm (talk) 13:33, 27 October 2021 (UTC)

Sign of discriminant never mentioned ?

I noticed that, oddly, the article never seems to mention that the formula $x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}$ is only valid if the discriminant $b^{2}-4ac$ is positive. Otherwise the right hand side of $(2ax+b)^{2}=b^{2}-4ac$ has no real root and the notation ${\sqrt {b^{2}-4ac}}$ makes no sense (unless you explicitly define the notation ${\sqrt {x}}$ as designating one of the two complex roots of $x$, but to my knowledge this notation is usually considered forbidden for numbers other than positive reals). Isn't this an important omission? So I tried to fix it --193.52.194.235 (talk) 11:10, 21 February 2022 (UTC)

Complex numbers exist... Joao003 (talk) 12:33, 17 May 2023 (UTC)

And if it's 0, you can just use one solution.......... Joao003 (talk) 12:36, 17 May 2023 (UTC)

Yes, √b² − 4ac, doesn't have an obvious principle value when b² − 4ac is not a non-negative real number. However ±√b² − 4ac, which is used in the quadratic formula, does meaningfully specify both square roots for all complex numbers. (Well, it's a double root for b² − 4ac = 0, but you know what I mean.) —Quantling (talk | contribs) 12:57, 17 May 2023 (UTC)

Savage16 20

There is a user named savage 1620 who had recently vandalised wikipedia page we request him to be blocked immediately David dclork li (talk) 13:38, 28 April 2023 (UTC)

Oh my... I'm sorry. I was to delete my post but for some reason intruded into yours and am not sure if I removed any of your text. The Wiki's editing system is something else... (It's bad.) I apologize. --ErrorCorrectionOfficer (talk) 00:22, 4 May 2023 (UTC)

The Egyptian Berlin Papyrus

@Graham87: I undid your edit because it left us with the same sentence twice in a row. I suspect that your intent was otherwise; please make another edit accordingly. —Quantling (talk | contribs) 12:54, 18 May 2023 (UTC)

I think I figured out the intended edit, and have made it. If I have failed, please accept my apologies. —Quantling (talk | contribs) 13:42, 18 May 2023 (UTC)

Nope, that's what I intended to do. Thanks! Graham87 14:27, 18 May 2023 (UTC)

A dubious equivalent formulation

On the Quadratic formula#Equivalent formulations section it says that the quadratic formula can be reduced to

$$x={\frac {-{\frac {b}{2}}\pm {\sqrt {\left({\frac {b}{2}}\right)^{2}-ac}}}{a}}$$It says that its dubious, which is quite strange, since it can be easily derived from the original quadratic formula:

${\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}=-{\frac {b}{2a}}\pm {\frac {\sqrt {b^{2}-4ac}}{2a}}=-{\frac {1}{a}}{\frac {b}{2}}\pm {\frac {1}{a}}{\frac {\sqrt {b^{2}-4ac}}{2}}$

$=-{\frac {1}{a}}{\frac {b}{2}}\pm {\frac {1}{a}}{\frac {\sqrt {b^{2}-4ac}}{\sqrt {2^{2}}}}=-{\frac {1}{a}}{\frac {b}{2}}\pm {\frac {1}{a}}{\sqrt {\frac {b^{2}-4ac}{2^{2}}}}$

$={\frac {-{\frac {b}{2}}\pm {\sqrt {{\frac {b^{2}}{2^{2}}}-{\frac {4ac}{2^{2}}}}}}{a}}={\frac {-{\frac {b}{2}}\pm {\sqrt {({\frac {b}{2}})^{2}-ac}}}{a}}$

I suggest removing the [dubious - discuss] tag, since its easily provable that this formulation is equivalent

Sincerely, ALonelyPhoenix (talk) 19:12, 21 September 2023 (UTC)

I made some edits to remove the dubious claim that these formulas are more useful when using a calculator. Now it says that they "may" be more useful. Also, I removed an intermediate result that wasn't useful, and generally shortened the section. What do you think? —Quantling (talk | contribs) 19:26, 21 September 2023 (UTC)

Yeah, now its less ambiguous and more compact, considering the intermediate result could be directly obtained by one factorization and the [dubious] tag made it seem like those two weren't equal lol

Thanks! ALonelyPhoenix (talk) 23:53, 21 September 2023 (UTC)

I took this version out entirely (leaving just one variant involving ${\tfrac {b}{2a}}$), since it wasn't clear what the point was of having multiple trivially distinct variant formulas, and no source was given for any of them. –jacobolus (t) 20:37, 18 February 2024 (UTC)

High-level structure

Hi @Quantling, I reverted your move of the 'history' section up to the top, because I don't think it's the friendliest start for an audience of laypeople or middle-/high-school algebra students. (I also couldn't find any reliable sources with "Sridharacharya's formula" and even in a general web search it seems pretty rare; I replaced the bold with italic.)

But the current first section is also not very good to lead with. My hope is to expand the § Geometric significance section, maybe retitled something less specific like "Meaning" or "Interpretation" or "Significance", and move that to the top. This section could elaborate about the meaning of the discriminant. It could maybe include "Special cases" as a sub-topic, which would try to demonstrate both symbolically and graphically what happens if a, b, and/or c = 0, what happens in the limit as these go infinite, etc..

The 'derivations' section was at some point in the past broken into two parts, with one ("completing the square") derivation on its own at the top, then other derivations later on in a separate section. Returning to that structure seems to me at least worth considering: Readers are likely to want to see some variant of the most common derivation near the top, but more examples can pretty safely be deferred in my opinion.

The history section can be much improved. It should be more specific/explicit about ancient Mesopotamian, Egyptian, Greek, Chinese, and Arabic/Persian methods, should talk about the way historically all of the quantities involved were considered to be non-negative, etc. It should elaborate about the specific contributions of Stevin, Descartes, and others, instead of just dropping names.

We should also ideally have some kind of section(s) about generalizations, applications, etc. down toward the bottom. And perhaps a section with some discussion about roots of quadratic equations with complex coefficients, maybe with image(s) showing a domain coloring plot of the complex plane.

I think the § By Lagrange resolvents sub-section should probably be pulled out of derivations (where it is similar to the previous subsection) and made into a new section nearer the bottom titled just "Galois theory" or "Lagrange resolvents".

We also could use more figures (and a replacement of the current SVG figure, which has broken rendering). I might make some figures using Desmos (probably just leave them as highish resolution png images), and link through from the image description pages for interactive versions.

–jacobolus (t) 19:04, 19 March 2024 (UTC)

I like the history section as first after the lede. Strangely, it is because it is not like the other sections and thus both, it makes the needle easier to find for those who are looking for it in the haystack, and it is easy to scroll past because it is smaller than the other sections combined, for those who are not looking for it. I admit that that isn't the strongest logic ... but perhaps we don't have to reinvent the wheel here, and there is some general Wikipedia advice on this topic? Also, over the years there have been many editors wanting to add Sridharacharya's formula or Sridharacharya's method (often in bold, though always reverted or otherwise diminished) so my gut tells me that it is real, and that there is value to having it somewhere near (or possibly in) the lede.

I agree that generalizations should be at/near the end. And proofs could be in a single section. —Quantling (talk | contribs) 20:19, 19 March 2024 (UTC)

I don't mind mentioning Sridharacharya's formula or similar, and I don't doubt that someone calls it this, but from the available sources I could find in a web search, I don't think the bold is justified: this doesn't seem like a widely adopted name, and I frankly don't think the attribution is justified considering how many different people through history have made various contributions to this topic. (Can you find any reliable sources mentioning this name specifically?)

I similarly took bold out of théorème d'Al-Kashi in Law of cosines § History (and took a mention thereof out of the lead section of that article), while also dramatically expanding the text so it's clear what Al-Kashi's version actually said and what it's relation is to the "modern" version, which I think is more useful than just naming things for some particular chosen person who made relevant contributions.

The § Historical development section here should similarly be significantly longer (3x the current length or more) to accurately and somewhat completely cover the topic, and I think it's substantially distracting to have as the first thing mentioned for an imagined struggling 14-year-old arriving here to figure out about the quadratic formula for their algebra class.

And proofs could be in a single section. – That is, you don't like my proposal that we consider putting one derivation near the front and deferring alternative derivations to further down the page? –jacobolus (t) 00:34, 20 March 2024 (UTC)

... putting one derivation near the front and deferring alternative derivations to further down the page. That works for me. Apologies for the confusion. —Quantling (talk | contribs) 17:19, 20 March 2024 (UTC)

Okay, I did such a split. Does that read okay? I think we should try to make a graphical depiction of completing the square section somewhat along the lines of File:Completing_the_square.svg, but using the expressions for a generic quadratic equation. I find the video File:Completing the square.ogv somewhat confusing though. –jacobolus (t) 03:45, 23 March 2024 (UTC)

Among the first few hits from Google, I see Sridharacharya Formula, Sridharacharya Formula - Definition, Derivation, Proof with Example, Shreedhara Acharya's formula, Why is the quadratic equation also called the Shri Dharacharya formula?. Certainly not as many hits as "quadratic formula" would give, but perhaps more than any other "<insert some other contributor's name> formula" search would give for this formula. Is there a way to find out how many users have searched the English Wikipedia for "Śrīdharācāryya formula", "Śrīdharācāryya method", or any of the spelling variations? —Quantling (talk | contribs) 17:32, 20 March 2024 (UTC)

Yeah, but these hits are a quora answer, a wiki largely duplicative of the material at Wikipedia, and two different exam coaching provider's websites who probably sourced their material from a web search. None of these are "reliable sources" by Wikipedia standards. I don't disagree that someone somewhere calls it this, but it doesn't seem like a very widespread name (at least, not in the scholarly literature). The reliable sources I have seen discussing "the Hindu method" or "Śrīdhara's rule" (e.g. Gupta 1966, Renfro 2007) are referring to the approach to completing the square by first multiplying by 4 times the quadratic coefficient to avoid fractions, not to the "quadratic formula" as such. (Though if you start with generic coefficients and then follow Śrīdhara's method of completing the square, or any other generic method of solving a quadratic equation, what you end up with is of course something equivalent to the quadratic formula.) –jacobolus (t) 17:46, 20 March 2024 (UTC)

I changed the heading of the relevant derivation to § Completing the square by Śrīdhara's method. –jacobolus (t) 05:01, 23 March 2024 (UTC)

Discriminant with a bullet list

@Number 3434, I reverted your change to make the paragraph in the lead about the discriminant into a bullet list. I think this is too visually heavy and distracting at that spot, but it might be worth adding a separate section discussing it in greater detail (though I still would recommend against using a bullet list where paragraphs will do). There used to be a bullet list in the version of this article from a few months ago, special:permalink/1208763608, but I found the lead to be too long; remember, some readers just want a quick overview. You might also want to try expanding the part about quadratics at Discriminant or the part about disciminants at Quadratic equation. –jacobolus (t) 16:02, 30 April 2024 (UTC)

Sources about the name of the quadratic formula in India/Brazil

Hi @Loodog, thanks for your interest in the history of the quadratic formula and its name around the world. I reverted addition of the (apparently somewhat common in Brazil) name Bhaskara's formula from the lead (and I similarly routinely revert additions of Sridharacarya's formula to the lead) partly because I think the attribution itself is fairly inaccurate/inappropriate, but also because if we start in on trying to attribute this to individual mathematicians or groups, we're going to have 2 paragraphs reprising the history section in the lead, which I don't think are relevant or useful enough to the main expected audience for this page to put right at the top.

I don't mind mentioning names commonly used in Brazil, India, etc. in the history section, but some of your sources are not appropriate – please stop adding them. testbook.com is some Indian test prep company and their webpage doesn't seems particularly expert or authoritative. The medium blog is a copy of a copy of an old version of Wikipedia – we can't cite it. Portuguese Wikipedia (or any version of Wikipedia) is a publicly editable wiki not usable as a source for us. The mathnasium.com page was copied from a different wiki, h2g2, which is also publicly editable and also not usable as a source. I haven't investigated mundoeducacao.uol.com.br but the page you linked is blanketed by spammy ads. I don't think it can be used as a reliable source. Please don't add these back to the article again.

The masters' theses are fine in my opinion: one is a Brazilian masters student who specifically did a review of the name/attribution for the quadratic formula in Brazilian textbooks, and the other is a masters student who wrote about what contributions Bhaskara II made to the solution of quadratic equations. The Juggernaut is also potentially fine (though the title makes it sound like the goal is mostly scoring nationalistic political points), but it's a paywalled magazine article that I can't read. (If you could add a direct quotation from that article it would be helpful; I can't tell what claim you are trying to verify with it). –jacobolus (t) 17:59, 27 September 2024 (UTC)

Hi and thanks for your contributions and diligence. As a non-Indian and non-Brazilian, I don't have any particular dog in this fight other than that this is verifiable information that enriches a wikipedia reader's world context in reading about these things. Actually, it's a bit fitting that the Juggernaut article's point was how discoveries made by non-Europeans tend to not get named for those people whereas Europeans do get things named after them. Pascal's Triangle is another example of this.Louiedog (talk) 15:50, 30 September 2024 (UTC)

@Loodog can you give an explicit quotation of the relevant passage from the Juggernaut article? I can't read it from here unless I set up a recurring payment of $14/month, and I have no personal interest in doing that. –jacobolus (t) 19:18, 30 September 2024 (UTC)

"...For instance, some Indian schools call the quadratic formula Sridharacharya's formula and some Brazilian schools call it Bhaskara's formula."Louiedog (talk) 21:26, 30 September 2024 (UTC)

Aha. Okay, we can use this as a source, and I'll add the quotation, though examples like those masters' theses are definitely more authoritative if anyone wants to follow up the details. –jacobolus (t) 02:54, 1 October 2024 (UTC)

It's no doubt true in many cases that discoveries made by non-Europeans tend to not get named for those people whereas Europeans do get things named after them. But we shouldn't use a pop-history magazine story to support a claim about any particular example of that. Oversimplified and exaggerated claims about the history of mathematics circulate endlessly in such places. XOR'easter (talk) 02:34, 1 October 2024 (UTC)