Show that there are infintely many pairs (a,b) of relatively prime integers (not necessarily positive) such that both the equations \begin{eqnarray*} x^2 +ax +b &=& 0 \\ x^2 + 2ax + b &=& 0 \\ \end{eqnarray*} have integer roots. quadraticsnumber theoryrelatively primeDiophantine equationalgebra unsolvedalgebra