Question

The product of two numbers is 63. They have a sum of -16. What are the numbers?

Answer 1

Numbers are `-7` and `-9`.

Explanation:

Let the numbers be `x` and `-16-x`

then `x(-16-x)=63`

i.e. `-16x-x^2=63`

or `x^2+16x+63=0`

i.e. `(x+7)(x+9)=0`

i.e. `x=-7` or `-9`

If `x=-7` then other number is`-16-(-7)=-9` and if `x=-9` then other number is`-16-(-9)=-7`

Hence numbers are `-7` and `-9`.