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**fardeen_gen** If $\displaystyle \color{blue}m^2 + n^2 - mn - m - n - 1\leq 0$, where $\displaystyle \color{blue}m,n\in\mathbb{R}$ and $\displaystyle \color{blue}z_{1},z_{2}$ be the complex numbers such that that $\displaystyle \color{blue}|z_{1}| \leq m, |z_{2}|\leq n$ and $\displaystyle \color{blue}a > (|z_{1}| - |z_{2}|)^2 + (\arg z_{1} - \arg z_{2})^2 - |z_{1} - z_{2}|^2$. If $\displaystyle f(x) = ax^2 + bx + c > 0$ for all $\displaystyle x$, show that $\displaystyle f(x) + f'(x) + f''(x) > 0$ for all real $\displaystyle x$.