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

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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

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Accepted Answer

David Goodmanson
David Goodmanson on 22 Nov 2020
Edited: David Goodmanson on 22 Nov 2020
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.

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