2013 HMMT Algebra #4: All Possible values of A
Source:
February 16, 2013
HMMTcomplex numbers
Problem Statement
Determine all real values of for which there exist distinct complex numbers , such that the following three equations hold:
\begin{align*}x_1(x_1+1)&=A\\x_2(x_2+1)&=A\\x_1^4+3x_1^3+5x_1&=x_2^4+3x_2^3+5x_2.\end{align*}