## Confusing the square

Here’s some further evidence, as if it were needed, that the disproportionate effort devoted in schools to coaching students to solve quadratic equations is largely wasted. The following were recently presented, independently and apparently in all seriousness, by two students each of whom has a respectable pass at Advanced Higher:

$ax^2 + bx + c = 0 \ \Longrightarrow \ x = \dfrac{b^2\pm\sqrt{4ac}}{2a}$.

$ax^2 + bx + c = 0 \ \Longrightarrow \ x = \dfrac{-b\pm\sqrt{4a-b^2}}{2ac}$.

Of course it’s not surprising that students who’ve been encouraged to memorise a formula but never taught to derive it come up with keech like this: the only remarkable phenomenon is how rarely it seems to happen. Possibly I ought to salute their teachers for not having wasted enough class time to burn the correct formula indelibly into these students’ brains; there’s just a chance that they may have been teaching them something worthwhile instead.