MathDB

2010 Algebra #4: Common Roots of Common Coefficients

Source:

July 15, 2012

complex numbers

Problem Statement

Suppose that there exist nonzero complex numbers

a

b

c

, and

d

such that

k

is a root of both the equations

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

and

bx^3+cx^2+dx+a=0

. Find all possible values of

k

(including complex values).