We can see in Equation (I) that x=0 is a root of the given equation. To find other roots, we will solve Equation (II). To do so, we need to define another variable. If we let z=x^2, we can rewrite Equation (II) in terms of the z-variable.
We found that the root of z^2+2z+1=0 is z=-1, which is the double root. This means that x^2=-1. Let's solve this equation! Remember that sqrt(- a)= sqrt(a)* i.
Since z=-1 was a double root, x=i and x=- i are also double roots.
Roots
x=0, x=i, x=i,
x=- i, x=- i
We can see that there are five roots. One of these is real and four of these are imaginary.
