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+2 votes
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.
in Calculus by Boss (17.6k points) | 162 views
I think option D
I also think (D) should be answer but not sure about it.
Solution given in the answer section

1 Answer

+3 votes
Best answer

Option D

by Loyal (9.8k points)
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you have written "if they are equal then $x_{0}$ has to be imaginary". Can you please explain this line. Complex numbers can't be compared. right ?

x0 will be imaginary because

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