What two numbers can be multiplied to be 60 and added to be - 16

Let us assume the two numbers to be "x" and "y".

Then

xy = 60

x = 60/y

And

x + y = - 16

Putting the value of "x" from the first equation in the second equation we get

x + y = - 16

(60/y) + y = - 16

y2 + 60 = - 16y

y^2 + 16y + 60 = 0

y2 + 10y + 6y + 60 = 0

y (y + 10) + 6 (y + 10) = 0

(y + 10) (y + 6) = 0

Then

y + 10 = 0

y = - 10

So

x = 60/y

= - (60/10)

= - 6

When

y + 6 = 0

y = - 6

Then

x = 60/y

= - (60/6)

= - 10

So the two unknown numbers are - 6 and - 10.