Find the zeroes of 6x^4+x^3+2x^2-4x+1

By the rational root theorem, you have the following candidates for roots:



Plugging in each of these will tell you which one is actually a zero. You'll find that both and both work, which means and are linear factors to the quartic.

To find the remaining factor(s), divide the quartic by the known factors:




Since has no real roots, you are left with



which has two real zeros at , . It also has two complex roots at .