# All real and complex roots of 10 degree polynomial [closed]

I am trying on $${\rm poly} =x^{10} + 7 x^9 - 38 x^8 - 192 x^7 + 209 x^6 - 1009 x^5 + 5768 x^4 - 19002 x^3 - 2580 x^2 - 99792 x^1 - 120960$$;

1. I was trying "FindRoot & NRoots" to find real and complex roots, but this doesn't work.

2. Does Mathematica have its own implementation of double roots?

• Reduce[x^10 + 7 x^9 - 38 x^8 - 192 x^7 + 209 x^6 - 1009 x^5 + 5768 x^4 - 19002 x^3 - 2580 x^2 - 99792*x^1 - 120960 == 0, x] Then type N[%]
– Moo
May 6 at 16:58
• Solve[poly==0,x] will return you all these roots. They are, however, not expressed in radicals. So, what are you going to do with them further? If you disclose that we will be able to help you further. May 6 at 18:13
• People here generally like users to post code as Mathematica code instead of just images or TeX, so they can copy-paste it. It makes it convenient for them and more likely you will get someone to help you. You may find the meta Q&A, How to copy code from Mathematica so it looks good on this site, helpful May 6 at 19:18
• And NSolve[poly==0,x] will return you numerical approximations of all these roots. May 6 at 19:19

Real roots.

Solve[{x^10 + 7 x^9 - 38 x^8 - 192 x^7 + 209 x^6 - 1009 x^5 +
5768 x^4 - 19002 x^3 - 2580 x^2 - 99792*x^1 - 120960 ==
0}, x, Reals]
%//N


Complex roots.

Solve[{x^10 + 7 x^9 - 38 x^8 - 192 x^7 + 209 x^6 - 1009 x^5 +
5768 x^4 - 19002 x^3 - 2580 x^2 - 99792*x^1 - 120960 == 0,
Im[x] != 0}, x]
%//N