An alternative quadratic formula (Q1985483)

This article deals with methods for solving quadratic equations, beginning with the ``Babylonian'' method and its geometric incarnations in Euclid's second book of the ``Elements''. The second section covers quadratic equations in fields of characteristic \(2\) as well as solution formulas involving trigonometric functions. In the last section, the symmetric solution formula \(x_{1,2} = (\sqrt{u-v} \pm \sqrt{u+v}\,)^2\) of the quadratic equation \(x^2 - 4ux + 4v^2 = 0\) is presented, together with a few remarks on the numerical stability of these solution formulas. This is a must-read for anyone teaching elementary algebra.