Question

How do you solve `(x-7)(x+2)=0` using the zero product property?

Answer 1

Either `x=7` or `x=-2`

Explanation:

Consider the quadratic function expressed as the product of two factors

`(x-a)(x-b)` with `{a, b} in QQ`

For this product to equal zero either `(x-a) = 0` or `(x-b) = 0`

In the example given in this question `a=7` and `b=-2`

Hence the zeros of `(x-7)(x+2)` are either `7` or `-2`

NB: When given any quadratic function for which you wish to find the zeros it is a good start to see if it factorises in this way