-1

When a coefficient of a polynomial varies , what is the locus of the roots in the Complex Plane?

Jean Marie
  • 88,997
Tim Neal
  • 1
  • 1
    See this question. – Dietrich Burde Dec 08 '17 at 19:16
  • You can "realize" any polynomial as the characteristic polynomial of a certain matrix. This looks artificial, at first view, but it is rather common and fruitful because much is known on roots which become eigenvalues and their stability. See for example one of my very recent answers: https://math.stackexchange.com/q/2547158 – Jean Marie Dec 08 '17 at 19:27

1 Answers1

1

Let's say the parameter $d$ is real. Then the locus has the implicit equation $\text{Im}((X+iY)^4 + a (X+iY)^3 +b (X+iY)^2 + c (X+iY)) = 0$.

Robert Israel
  • 470,583
  • Dear Teacher and Dear Professor, can you look my problem, if you have few minutes, please. My solution is insufficient, but I dont know what's missing. Can you help/edit my question/solution for me? Best regards. Thank you so much. – – MathLover Dec 11 '17 at 21:48
  • https://math.stackexchange.com/questions/2559814/is-the-proof-i-am-using-sufficient-for-the-system-of-equation – MathLover Dec 11 '17 at 21:49