Problem related to a polynomial
I am stuck on the following problem:
I see that $\color{green}{|P(0)| \leq C}$ and so option 4 can be
eliminated. If I take $\color {red}{P(x)=1+x^2 }\,\,\text{and} \,\,\color
{blue}{C=1 >0}$,then also the given relation is satisfied and hence option
1 can not be right. From the given options, 2 appears to be correct choice
but I do not know how to show it.
Can someone explain? Thanks and regards to all.
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