IMO Shortlist 1982 problem 4
Determine all real values of the parameter
for which the equation
has exactly four distinct real roots that form a geometric progression.
%V0
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.
Source: Međunarodna matematička olimpijada, shortlist 1982
Školjka 
