Question

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

Answer 1

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.