Question

The product of two consecutive positive integers is 120. How do you find the integers?

Answer 1

There is no such positive integer.

Explanation:

Let the integer be `x`. Then next integer is `x+1` and as their product is `120`, we have

`x(x+1)=120` or

`x^2+x=120`

`x^2+x-120=0`

As discriminant, (`b^2-4ac` if the equation is `ax^2+bx+c=0`) is

`1^2-4*1*(-120)=1+480=481` is not a perfect square, meaning thereby no rational solution,

there is no such positive integer.