Question 79
Let $f(x) = x^{2} - a x + a^{2} - 4$, where $a$ is a real number. Find all $a$, for which:
a) the equation $f(x) = 0$ has two real roots $x_{1}$ and $x_{2}$ such that $|x_{1}^{3} - x_{2}^{3}| \leq 4$;
b) the inequality $f(x) \geq 0$ holds for all integers $x$.
a) the equation $f(x) = 0$ has two real roots $x_{1}$ and $x_{2}$ such that $|x_{1}^{3} - x_{2}^{3}| \leq 4$;
b) the inequality $f(x) \geq 0$ holds for all integers $x$.