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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.

1 Answer

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Option D

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