IMO Shortlist 1982 problem 4
Dodao/la:
arhiva2. travnja 2012. Determine all real values of the parameter
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
for which the equation
![16x^4 -ax^3 + (2a + 17)x^2 -ax + 16 = 0](/media/m/6/9/2/692068c31df4591be2a33afec9ede6bf.png)
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.
Izvor: Međunarodna matematička olimpijada, shortlist 1982