A system of two quadratic equations
Source: Germany 2017, Problem 1
May 4, 2017
quadraticssystem of equationsequationquadratic equationalgebraalgebra proposedGermany
Problem Statement
Given two real numbers and , we study the following system of equations with variables :
\begin{align*} x^2+py+q&=0,\\
y^2+px+q&=0.
\end{align*}
Determine the number of distinct solutions in terms of and .