Suppose for an equation say –
For proving Infinite solutions ,
Assume the existence of a non-trivial solution by keeping one of the variables fixed or a constant, Now the equation is in one variable.
Since the equation is a quadratic , there should exist another root .
Similarly for the other root there exists another root… thus there exists infinite roots.
That is … in
If b is a constant ,
is a quadratic.
Hence we can find two roots.
let roots be
Now keep fixed and b as a variable ,
This again has two roots.
Thus , this way .. the equation has infinite roots.