The Zero-Product Property
You may have noticed that when we were solving linear equations we came up with a maximum of one solution. You will find that when we solve quadratic equations we will come up with a maximum of two real solutions. There are also special cases when there is one real solution and at times there is no real solution. We will delve deeper into this discussion when we talk about Discriminants. Until then, how do we find these solutions?
One way is to use the Zero-Product Property. This property says that if ab = 0 then a = 0 or b = 0. If two numbers or two algebraic expressions are multiplied together and the answer is 0, then one of those numbers or expressions has to be zero.
This property will help us a great deal in solving quadratic equations.