Alternate form of equation is$:$
$x(x+2)(x^{2}+2x-6)=0$ $\text{ or }$ $x(x^{3}+4x^{2}-2x-12)=0$
As $p(x) = \alpha$
Roots of the equation $\text{or}$ value of $\alpha$ are$:$
$x = - 2, x = 0, x = - 1 - \sqrt{7}, x = \sqrt{7} -1$
$p(-3) = - 9$
$p(-1) = 7$
Hence option $\text{D}$ is correct.