Roots:-3i, double root at 3

Question

Write a polynomial function. Give answer in standard form.

Answer 1

(x - 3i) (x+ 3i) (x -3 ) (x-3) = (x^2 +3) (x^2 - 6x +9) = x^4 - 6x^3 +9x^2 + 3x^2 -18x +27 = x^4 -6x^3 +12 x^2 -18x +27. If -3i is a root,the conjugate 3i must be a root. Double root means it is multiplied together twice. Multiplying the complex conjugate terms yields a real expression.