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.

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