If a,b,c,d are the roots of the equation x4-2πx-2019=0, then the product of a+b+cabc,b+c+dbcd,c+d+acda,d+a+babd is equal to

Given equation is x4-2πx-2019=0------(1) Since a,b,c,d are the roots of equation (1), then  Sum of the roots S1=a+b+c+d=0-------(2) Product of the roots S4=abcd=2019------(3)Now from equation (1)  ,a+b+c=−db+c+d=−ac+d+a=−bd+a+b=−c[SolutionStep4]:∴ Required Product =a+b+cabcb+c+dbcdc+d+acdad+a+badb=−dabc−abcd−bcda−cabd=1abcd2=12019∵ from equation3