Answer
The set of all whole numbers (i.e. integers) is countable. Hence, the set of all three-tuples in $(a,b,c)$ is countable too
Work Step by Step
All whole numbers (i.e. integers) is countable. Hence, the set of all three-tuples in $(a,b,c)$ is countable too so that we can list all three tuples:
so equation whose coefficients are formed by {$a(j),b(j),c(j)$},$ j$ runs from $1$ to infinity, there corresponds, in general, at most $2$ real roots $x$ and $ y$.
Mark them as $x_{1}$ and $y_{j}$.
Then we have a set of pairs {$x_{1}, y_{1}$} {$x_{2}, $y_{2}$}.... which is countable.
