How would you go about finding the roots of the polynomial: $$x^4 +5x^3+4x^2+6x-4=0.$$
I attempt to form two quadratics e.g. $$(x^2+ax+b)(x^2+cx+d)$$ and then tried to expand, collect like terms, and solve for the coefficients simultaneously, but this results in a hard system of equations.
I was wondering if there was a better approach to this question.
Any help would be greatly appreciated.