Show that there are infinitely many pairs(a,b) of relatively prime integers (not necessarily positive) such that both quadratic equations x²+ax+b=0 and x²+2ax+b=0 have integer roots
I have no idea on how to solve the question. The only thing I tried was trying to look at the discrimants of the equations which must be perfect squares for the roots to be integer. The discrimants are a²-4b=m² and 4a²-4b=n².. I got no further