Find the roots of x^4 + 6x^3 + 17x^2 + 22x + 14 = 0

Question

anonymous · Answer

I feel stupid, but no idea how to factor this right. All the roots are complex, so there is no nice rational zeros theorem method or anything, but I know it's something that comes out "clean", just no idea how to do this kind of factoring.

anonymous · Answer

Refer to the Mathematica9 attachment that includes a plot.

campbell_st · Answer

well as a quick tip, you can graph the curve and see if there are zeros https://www.desmos.com/calculator before you attempt to find them... it may save time andstress https://www.desmos.com/calculator is a great graphing site

anonymous · Answer

Well, I actually need to be able to find those zeros by hand in this case. It was the characteristic polynomial for:
$$y^{(4)}+6y'''+17y''+22y+14 = 12sint + e^{-t}$$
So not exactly a situation where I can dismiss the problem just because there are no real zeros, I do these need those complex zeros so I can have a complementary solution and not just a particular solution.