Maths
posted by OIan on .
The function f(x)=x^4−15(x^3)+81(x^2)−201x+182 has four complex roots, one of which is 3−2i. What is the sum of all real and imaginary coefficients of these roots?
Details and assumptions
i is the imaginary unit, where i2=−1.

one other complex root must be 3+2i
So, (x(32i))(x(3+2i)) are factors of f(x)
That is, (x3)^2+4 = (x^26x+13) divides f(x)
f(x) = (x^26x+13)(x^29x+14)
= (x^26x+13)(x2)(x7)
So, the roots are
2,7,32i,3+2i
You can add 'em up