Question 976543
You will find among possible rational and real roots, NO real roots.  Try according to synthetic division and rational roots theorem, testing plus and minus of 1,2,3,6, 1/2, 1/4, 3/2,3/4.  None will give zero remainder.


Solving for x^2 using general solution for quadratic formula, find {{{x^2=-1/4}}}  or {{{x^2=-6}}}.


From these, continue on to find x values for the four imaginary roots.
Roots are {{{system(-i/2, i/2, -i*sqrt(6), i*sqrt(6))}}}.