My usually understanding tells me that an algebraic equation can intersect the x-axis, touch it, or not touch it. In which cases I will get a real root, coinciding real root, and an imaginary root (conjugate pair) respectively.
Note that I am considering real coefficients only.
But consider the following:
The quadratic equation $p(x) = 0$ with real coefficients has purely imaginary roots. Then the equation $p(p(x)) = 0$ has what type of roots?
Since $p(x)$ can become zero only on input of some complex numbers, I get the sense that the roots of the equation $p(p(x)) = 0$ will also be imaginary. But this is all based on intuition.
The answer provided to me was that The roots are neither real nor purely imaginary. Then what are the roots? I mean they must be either real or imaginary.
All help will be appreciated!