 This is because the complex roots are complex conjugates and hence are symmetric about the real axis.In celestial mechanics, the three-body problem has been studied in the special case that the three bodies form an isosceles triangle, because assuming that the bodies are arranged in this way reduces the number of degrees of freedom of the system without reducing it to the solved Lagrangian point case when the bodies form an equilateral triangle.The first instances of the three-body problem shown to have unbounded oscillations were in the isosceles three-body problem.