A quadratic whose discriminant is a square is answered with the square left under the root #2140

solve::z::a*z^2 - (a^2 - b*c)*z - a*b*c = 0
→ { (a ^ 2 + -b * c - sqrt((-(a ^ 2 + -b * c)) ^ 2 - 4 * a * -a * b * c)) / (2 * a), … }

The discriminant is (a^2 + b*c)^2, and the roots are a and -b*c/a. collapse factors the same polynomial as (a - z) * (-a * z - b * c), while factor::z::… is refused.

In Modenov's Problems in Geometry (#2131), every second intersection of a line with the unit circle is a quadratic of this kind with one known root.