Let \(f(x,y)\) be a real homogeneous polynomial of degree \(n \geq 3\) without multiple roots in \(\mathbb{C}\). In the paper under review the authors prove that \(f\) has all real roots if and only if for any \({(\alpha,\beta)\in\mathbb{R}^2{\setminus}\{0\}}\) the polynomial \(\alpha f_x + \beta f_y\) has \(n - 1\) distinct real roots. This result answers to a question of P. Comon and G. Ottaviani [On the typical rank of real binary forms, arXiv:math/0909.4865] and allows to complete their argument to show that a real binary form \(f\) has symmetric rank \(n\) if and only if it has \(n\) distinct real roots.