BG-MO 1985 Problem 2

Find all real parameters $a$ for which all the roots of the equation $x^6+3x^5+(6-a)x^4+(7-2a)x^3+(6-a)x^2+3x+1$ are real.

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.