Can someone suggest some most difficult questions on polynomials that would be of any standard but please they must be difficult.and sooner

Try to search on net. By the way, u live in which state ??
i dont think these are being held here.
in up
and what about you
I dont know of UP.. They must be held. Look on net and search for RMO co ordinators and see UP state


Let p and q be the roots of the polynomial m x^{2} +x(2-m) +3. Let  m_{1} and  m_{2} be two values of m satisfying  \frac{p}{q} +  \frac{q}{p} =  \frac{2}{3}   . Determine numerical values of  \frac{ m_{1} }{  m_{2} ^{2} } +  \frac{ m_{2} }{   m_{1} ^{2}  } .

FYI answer is 99.