Best rank k approximation for binary forms

In the tensor space ${\mathrm{S}\mathrm{y}\mathrm{m}}^d{\mathbb{R}}^2$ of binary forms we study the best rank $k$ approximation problem. The critical points of the best rank $1$ approximation problem are the eigenvectors and it is known that they span a hyperplane. We prove that the critical points of the best rank $k$ approximation problem lie in the same hyperplane.