Problem
ALG-B1-M04-P008 Discriminant and Distance
#8
★★★☆☆ Level 3 of 5
Let \(u,v\) be the roots of a monic quadratic trinomial. Prove that its discriminant equals \((u-v)^2\).
Write the trinomial as \(x^2-(u+v)x+uv\).
The discriminant equals \((u+v)^2-4uv=u^2-2uv+v^2=(u-v)^2\).
This fact often shortens computations.