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This article starts with an error: it's a third degree equation that can have real solutions whose calculation may involve the square root of negative numbers.

• ColinWright 14y ago
  What you're talking about is that cubics can have real solutions, and yet require square roots of negative numbers while following the formula. This is true, and it is, in fact, what historically led people to start to take complex numbers seriously. However, the article never talks about real solutions of quadratics requiring square roots of negative numbers. The article only talks about it turning out all right in the end. What they mean is this. Suppose you allow square roots of negative numbers, and simply work with them using the usual laws of algebra. Sometimes you have a quadratic that results in a solution that has the square roots of negative numbers, and hence the "solution" seems to have no interpretation. However, substituting back into the original equation we can see that they are, in some sense, genuine solutions. So I would claim that the article is actively misleading to those who already know some of the history, and is less "complete" than it might be, but it avoids talking about cubics, and with a strict and literal reading is accurate. I'm not, by the way, defending it. I wrote a similar article many years ago, and I did use the cubic example, including showing how to solve a cubic. It was aimed at a slightly ore sophisticated audience, however, and I'm not convinced this article is "wrong" in any important sense.