  We show that the spectrum of every $\mathbb{R}-$isotropic homogeneous binary
form $P$ of degree $n\geq3$ is an interval of the form $[0,M_P],$ where $M_P$
is some positive constant. This completes the discussion around a conjecture of
Mordell from 1940 (disproved by Davenport) regarding the existence of spectral
gaps for binary cubic forms and further settles Mahler's program for binary
forms of every degree.
