Posted by OIan on Tuesday, April 16, 2013 at 3:33am.
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.

Maths  Steve, Tuesday, April 16, 2013 at 11:08am
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
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