CZ-SK-MO 1954 Problem 1

Solve the equation $ax^2+2(a-1)x+a-5=0$ in real numbers with respect to (real) parametr $a$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.