Question 142
Let $c$ be a given real number. Suppose that for all real numbers $a$ and $b$ the function $f(x) = x^2 - 2a x + b$ satisfies the following inequality
$$
f(c) \cdot f(-c) \geq f(a).
$$
Find all possible values of $c$.
$$
f(c) \cdot f(-c) \geq f(a).
$$
Find all possible values of $c$.