Let m and $$\mathrm{n}$$ be the numbers of real roots of the quadratic equations $$x^{2}-12 x+[x]+31=0$$ and $$x^{2}-5|x+2|-4=0$$ respectively, where $$[x]$$ denotes the greatest integer $$\leq x$$. Then $$\mathrm{m}^{2}+\mathrm{mn}+\mathrm{n}^{2}$$ is equal to __________.

Let $$\alpha_1,\alpha_2,....,\alpha_7$$ be the roots of the equation $${x^7} + 3{x^5} - 13{x^3} - 15x = 0$$ and $$|{\alpha _1}| \ge |{\alpha _2}| \ge \,...\, \ge \,|{\alpha _7}|$$. Then $$\alpha_1\alpha_2-\alpha_3\alpha_4+\alpha_5\alpha_6$$ is equal to _________.

Let $$\alpha \in\mathbb{R}$$ and let $$\alpha,\beta$$ be the roots of the equation $${x^2} + {60^{{1 \over 4}}}x + a = 0$$. If $${\alpha ^4} + {\beta ^4} = - 30$$, then the product of all possible values of $$a$$ is ____________.