OME 2021 Problem 4

Let $a,b,c,d$ real numbers such that: $$a+b+c+d=0 \text{ and } a^2+b^2+c^2+d^2 = 12$$ Find the minimum and maximum possible values for $abcd$ , and determine for which values of $a,b,c,d$ the minimum and maximum are attained.