Comments by "Harry Mills" (@harrymills2770) on "Can you crack this beautiful equation? – University exam question" video.

  1. Teach your students to compute the discriminant before wasting time on the entire quadratic formula. If you're only looking for real solutions, b^2 - 4ac < 0 means you're done looking. I teach my students to simplify b^2 - 4ac and simplify its square root as much as possible, before plugging into the quadratic. But invariably, they've received prior cookbook training by other instructors so they always write the whole formula out and then mess up because they're carrying all the extra junk along. Worse, all the extra junk makes them want to shortcut the work, until what they're writing bears no resemblance to the truth. All math should proceed from one truthful statement to the next.
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