$P(x)=ax^2+bx+c$ has exactly $1$ different real root where $a,b,c$ are real numbers. If $P(P(P(x)))$ has exactly $3$ different real roots, what is the minimum possible value of $abc$?

$ 
\textbf{(A)}\ -3
\qquad\textbf{(B)}\ -2
\qquad\textbf{(C)}\ 2\sqrt 3
\qquad\textbf{(D)}\ 3\sqrt 3
\qquad\textbf{(E)}\ \text{None of above}
$
1. Given that \( P(x) = ax^2 + bx + c \) has exactly one real root, we know that the discriminant of \( P(x) \) must be zero. The discriminant of a quadratic equation \( ax^2 + bx + c \) is given by:
   \[
   \Delta = b^2 - 4ac
   \]
   For \( P(x) \) to have exactly one real root, we must have:
   \[
   \Delta = 0 \implies b^2 - 4ac = 0
   \]

2. Since \( P(x) \) has exactly one real root, it can be written in the form:
   \[
   P(x) = a(x - k)^2
   \]
   where \( k \) is the root of \( P(x) \).

3. We need to find the minimum possible value of \( abc \) given that \( P(P(P(x))) \) has exactly 3 different real roots. First, let's express \( P(P(x)) \):
   \[
   P(P(x)) = a(P(x) - k)^2 = a(a(x - k)^2 - k)^2
   \]

4. Now, we need to find \( P(P(P(x))) \):
   \[
   P(P(P(x))) = a(P(P(x)) - k)^2 = a\left(a(a(x - k)^2 - k)^2 - k\right)^2
   \]

5. For \( P(P(P(x))) \) to have exactly 3 different real roots, the polynomial \( Q(x) = a\left(a(x - k)^2 - k\right)^2 - k \) must have exactly 3 roots. Since \( Q(x) \) is a polynomial of degree 4, one of the roots must be repeated.

6. The repeated root must also be a root of the derivative \( Q'(x) \). Let's find \( Q'(x) \):
   \[
   Q(x) = a\left(a(x - k)^2 - k\right)^2 - k
   \]
   \[
   Q'(x) = 4a^2\left(a(x - k)^2 - k\right)(x - k)
   \]

7. For \( Q'(x) = 0 \), we have two cases:
   \[
   4a^2\left(a(x - k)^2 - k\right)(x - k) = 0
   \]
   This implies either \( x = k \) or \( a(x - k)^2 - k = 0 \).

8. Since \( k \neq 0 \), we solve \( a(x - k)^2 - k = 0 \):
   \[
   a(x - k)^2 = k \implies (x - k)^2 = \frac{k}{a} \implies x - k = \pm \sqrt{\frac{k}{a}}
   \]
   \[
   x = k \pm \sqrt{\frac{k}{a}}
   \]

9. Therefore, the roots of \( P(P(P(x))) \) are \( k \), \( k + \sqrt{\frac{k}{a}} \), and \( k - \sqrt{\frac{k}{a}} \).

10. To find the minimum possible value of \( abc \), we use the fact that \( P(x) = a(x - k)^2 \). Expanding this, we get:
    \[
    P(x) = ax^2 - 2akx + ak^2
    \]
    Comparing with \( P(x) = ax^2 + bx + c \), we have:
    \[
    b = -2ak, \quad c = ak^2
    \]

11. Using the condition \( b^2 - 4ac = 0 \):
    \[
    (-2ak)^2 - 4a(ak^2) = 0 \implies 4a^2k^2 - 4a^2k^2 = 0
    \]
    This condition is satisfied.

12. To minimize \( abc \):
    \[
    abc = a(-2ak)(ak^2) = -2a^2k^3
    \]
    Using \( k = \frac{1}{a} \):
    \[
    abc = -2a^2\left(\frac{1}{a}\right)^3 = -2a^2 \cdot \frac{1}{a^3} = -2 \cdot \frac{1}{a} = -2
    \]

The final answer is \(\boxed{-2}\)