Given,

$p\left(x\right)=x^4+a{x}^3+b{x}^2+cx+d$

It is passing through $\left(1,0\right)$

Hence, $p\left(1\right)=0$

$\Rightarrow a+b+c+d=0$

It is passing through $\left(0, 2\right)$. Hence, we get,

$\Rightarrow p\left(0\right)=2$

 $\Rightarrow d=2$

The product of all the roots of the bi-quadratic equation is given as,

a constant term/coefficient of $x^4$$=2$

From the graph given, we can see that the real roots of $p\left(x\right)$ are given as,

$x=1, 2$ (as it intersects the real axis at $\left(1, 0\right)$ and $\left(2, 0\right)$)

Thus, the product of the real roots is $2$.

Hence, the product of the imaginary roots can be given as,

Product of all the roots/Product of real roots.

$=\frac{2}{2}$

$=1$