Q:

Mathematica shows complex roots while asked for reals?

I ran the following code in Mathematica
ToRadicals[Reduce[-14848 c^4 + 38016 c^3 x - 30888 c^2 x^2 + 6480 c x^3 + 1215 x^4 == 0 && c < 0,x,Reals]]

This should give the real roots of the polynomial. However, the output displays two complex roots? How is this possible?
Thanks in advance!e

A:

I am getting this
ToRadicals@
 Reduce[-14848 c^4 + 38016 c^3 x - 30888 c^2 x^2 + 6480 c x^3 + 
     1215 x^4 == 0 && c < 0, x, Reals]

addendum
Interesting, without ToRadicals one get only real roots.
f = -14848 c^4 + 38016 c^3 x - 30888 c^2 x^2 + 6480 c x^3 + 1215 x^4;
sol = Reduce[f == 0 && c < 0, x, Reals]

sol[[2]] /. c -> -1 // N
(* x == -1.12557 || x == 8.69121 *)

Manipulate[
 Plot[-14848 c^4 + 38016 c^3 x - 30888 c^2 x^2 + 6480 c x^3 + 
   1215 x^4, {x, -10, 10}], {c, -10, -0.1}]

