Algebra-1

$f'(x)=54x^4-6f(x)$ . Let $f(\alpha)=0$ , then $f'(\alpha)=54 \alpha^4 \implies f'(x)$ is non-negative wherever $f(x)=0$ . Since the function tends to $\infty$ as $x \rightarrow \infty,-\infty$ , the graph can never intersect the $x-$ axis. Hence number of distinct roots $= \boxed{0}$ .