Let $a$ be a fixed real number. Consider the equation $$(x + 2)^{2}(x + 7)^{2} + a = 0, \quad x \in \mathbb{R},$$ where $\mathbb{R}$ is the set of real numbers. For what values of $a$, will the equation have exactly one double-root?
Let $a$ be a fixed real number. Consider the equation
$$(x + 2)^{2}(x + 7)^{2} + a = 0, \quad x \in \mathbb{R},$$
where $\mathbb{R}$ is the set of real numbers. For what values of $a$, will the equation have exactly one double-root?