MathDB

Complex Roots

Source:

December 22, 2005

algebrapolynomialVietacomplex numbers

Problem Statement

For certain real values of

a, b, c,

and

d,

the equation

x^4+ax^3+bx^2+cx+d=0

has four non-real roots. The product of two of these roots is

13+i

and the sum of the other two roots is

3+4i,

where

i=\sqrt{-1}.

Find

b.