Question

What number multiplies to -5 and adds up to 6

Answer 1

The two numbers are
`3-√(14)` and
`3+√(14)`.

Explanation:

I am assuming you meant "numbers", otherwise you question has no answer.

Let us call the two numbers
`a` and
`b`, then we have

(1).
`ab =-5` (they multiply to -5)

(2).
`a+b =6` (they add to 6}

We solve for
`a` and
`b`, by first solving for
`a` in equation (1):

`a = -(5)/(b)`

and substituting this value into equation (2):

`-(5)/(b)+ b =6`

multiply both sides by
`b` and rearrange to get:

`-5+b^2 =6b`

`b^2-6b-5=0`

Using the quadratic formula we solve for
`b` to get:

`b = 3+ √(14)`

`b =3-√(14)`

which when put into equation (1) give

`a = 3-√(14)`

`a = 3+√(14)`.

Thus, the two numbers are
`3-√(14)` and
`3+√(14)`.