Consider trinomial $x^2 + bx + c = 0$. When $b = 205$ and $c = -206$, then $x = 1$ and the function evaluates to a perfect square. My question is, how can I choose $b$ and $c$ and generate functions that are always a perfect square? I tried trial and error but couldn't find a mathematical way to solve the problem. Note that $a$ is always equal to $1$, we need to choose $b$ and $c$.
$$x^2 + 205x -206 = 0$$