The number of real solutions of $x^7+5x^3+3x+1=0$ is equal to _________

$\mathrm{f}\left(\mathrm{x}\right) = {\mathrm{x}}^7+5{\mathrm{x}}^3+3\mathrm{x}+1$
${\mathrm{f}}^{\text{'}}\left(\mathrm{x}\right) = 7{\mathrm{x}}^6+15{\mathrm{x}}^2+3 = 0$
f is strictly increasing function
$\Rightarrow \mathrm{f}\left(\mathrm{x}\right) = 0 \mathrm{has} \mathrm{only} \mathrm{one} \mathrm{solution}.$