Let common root condition of equations $2a{x^3} + b{x^2} + cx + d = 0$ and $2a{x^2} + 3bx + 4c = 0$ be ${(\lambda bc + ad)^2} = {9 \over 2}(\mu bd + 4{c^2})(m{b^2} - nac),\lambda ,\mu ,m,n \in N$. If the equation ${\left( {{{mx} \over {1 + {x^2}}}} \right)^2} + k\left( {{{nx} \over {1 + {x^2}}}} \right) + \lambda - \mu = 0$ has exactly two real roots which are distinct, then the set of possible real value of $k$ is