Solve for the constants of a Quartic given the complex roots?

I am trying to solve the following quartic for a,b,c,d:

(x)^4 + a*(x)^3 + b*(x)^2 + c*(x) + d = 0

given that four of the roots are:

x= -5

x= -6

x= -9.6+25.7i

x= -9.6-25.7i

I have tried solve, linsolve, and vpasolve

Answer 1

[David Goodmanson]

Hi Johnathan,

r = [-5 -6 -9.6+25.7i -9.6-25.7i];
p = poly(r)
r1 = roots(p)   % check
p = 1.0e+04 *
    0.0001    0.0030    0.0994    0.8855    2.2580       % 1, a, b, c, d
r1 =
  -9.6000 +25.7000i
  -9.6000 -25.7000i
  -6.0000 + 0.0000i
  -5.0000 + 0.0000i

roots and poly are inverses of each other.

[Jonathan Green]

Thank you!!