Question

Why does the zero product property work?

Answer 1

If `a cdot b=0`, then at least one of `a` and `b` must be zero since if `a` and `b` were nonzero, then `a cdot b` would be nonzero; therefore,

`a cdot b=0` means that `a=0`, `b=0`, or both.

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I hope that this was helpful.