162 views
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 | 162 views
+1
I think option D
0
I also think (D) should be answer but not sure about it.
0
Solution given in the answer section

Option D

by Loyal (9.8k points)
selected
+1
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 ?
+2

x0 will be imaginary because

+1 vote