  We show that a real homogeneous polynomial f(x,y) with distinct roots and
degree d greater or equal than 3 has d real roots if and only if for any (a,b)
not equal to (0,0) the polynomial af_x+bf_y has d-1 real roots. This answers to
a question posed by P. Comon and G. Ottaviani, and shows that the interior part
of the locus of degree d binary real binary forms of rank equal to d is given
exactly by the forms with d real roots.
