We could use Viete expressions. They make the link between coefficients and roots in a given equation.
For example, if the equation is :
a*x^4 + b*x^3 + c*x^2 + d*x + e=0
x1 + x2 + x3 + x4=-b/a
In our equation, the coefficient b for x^3 is = 0, so
x1 + x2 + x3 + x4 = 0/1
x1 + x2 + x3 + x4=0