Let $a$ and $b$ be integers, $$P(x) = x^{3} + ax^{2} + bx - 2$$ It is known that the polynomial has exactly one real root. If $\mathbf{P}(1) = 0$, what is the smallest value that the integer $a$ can take? A) $-6$ B) $-5$ C) $-4$ D) $-3$ E) $-2$
Let $a$ and $b$ be integers,
$$P(x) = x^{3} + ax^{2} + bx - 2$$
It is known that the polynomial has exactly one real root.
If $\mathbf{P}(1) = 0$, what is the smallest value that the integer $a$ can take?
A) $-6$
B) $-5$
C) $-4$
D) $-3$
E) $-2$