If two real polynomials $f(x)$ and $g(x)$ of degrees $m\;(\geq2)$ and $n\;(\geq1)$ respectively, satisfy
$f(x^{2}+1) = f(x)g(x)$ $,$
for every $x\in \mathbb{R}$ , then
(A) $f$ has exactly one real root $x_{0}$ such that $f'(x_{0}) \neq 0$
(B) $f$ has exactly one real root $x_{0}$ such that $f'(x_{0}) = 0$
(C) $f$ has $m$ distinct real roots
(D) $f$ has no real root.