ILL 1982 Problem 14

Determine all real values of the parameter $a$ for which the equation $16x^4 -ax^3 + (2a + 17)x^2 -ax + 16 = 0$

has exactly four distinct real roots that form a geometric progression.

Dataset text AoPS wiki problems. 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.