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^2-8z+16=0 is z=4, which is the double root. This means that x^2=4. Let's solve this equation by taking the square root.
x^2=4 ⇔ x = ± 2
Since z=4 was a double root, x=2 and x=-2 are also double roots.
Roots
x=0, x=2, x=2,
x=-2, x=-2
We can see that there are five roots. All of them are real.
