Finding real and imaginary roots from polynomials
If a polynomial has a factor such as $(x-a)^n$ it is named as multiplicity, not an imaginary root. Imaginary root is when delta<0.
For example let $(x^2+1)(x-2)^2=0$
Here you have imaginary roots $i$ and $-i$ from $(x^2+1)$ and double roots $2$ and $2$ from $(x-2)^2$.