What two numbers multiply to -28 and add to 1?

Question

What two numbers multiply to -28 and add to 1?

Answer 1

let x and y be the numbers

xy=-28

x+y=1, y=1-x

x(1-x)=-28

x-x^2=-28

x^2-x-28=0

use the quadratic formula

(1±√(1+112))/2

(1±√113)/2

the numbers are (1+√113)/2 and (1-√113)/2

when you add you get (2+√113-√113)/2=2/2=1

when you multiply you get (1+√113-√113-113)/4=-112/4=-28