Let $\mathrm{f} : \mathrm{R}\to \mathrm{R}$ be a continuous onto function satisfying $\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}(-\mathrm{x})=0\mathrm{\forall }\mathrm{x}\in \mathrm{R}$. If $\mathrm{f}(-3)=2\text{ and }\mathrm{f}\left(5\right)=4\text{ in }[-5, 5]$, then the minimum number of roots of the equation f(x) = 0 is _______.

$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}(-\mathrm{x})=0$

Therefore, f(x) is an odd function.

Since points (-3, 2) and (5, 4) lie on the curve, (3,-2) and (-5, -4) will also lie on the curve.

For minimum number of roots, graph of continuous function f(x) is as follows:

From the above graph of f(x), it is clear that equation f(x) = 0 has at least three real roots.