https://www.poshenloh.com/quadratic
Mathematician figures out a simpler way to solve a quadratic equation. Algebra 1 students everywhere rejoice?
I love the work Po-Shen is doing on math education, from Expii for middle school students through MOP and coaching IMO. He sponsors the competition team my daughter joined in 8th grade, where she’s worked alongside talented students up through a multi-time IMO Gold Medalist.
Getting students thinking along the lines of these fundamental approaches (difference of squares, Vieta’s formula and others are buried in this simple method) would certainly serve as a better foundation than guess and check or plugging into the magic quadratic formula (which few students every actually derive to understand).
If you ever get to see him speak at a conference or competition, I highly recommend it.