Question

The product of two consecutive integers is zero, find the integers. Show work

Answer 1

0,1

Explanation:

Let n represent the first interger. and n+1 represent the next interger.

`n * (n + 1) = 0`

`{n}^(2) + n = 0`

Complete the square.

`( (n)/(2) {)}^(2) = \frac{ {n}^(2) }{4}`

`{n}^(2) +n + \frac{ {n}^(2) }{4} = \frac{ {n}^(2) }{4}`

`(n + (n)/(2) ) {}^(2) = \frac{n {}^(2) }{4}`

Take the square root.

`(n + (n)/(2) ) = (n)/(2)`

`n = 0`

Plug 0 in for 0+1.

`0 + 1 = 1`

So the consective intergers are 0,1.