What two numbers have a product of -36 and a sum of -5?

Answer 1

one number is -9, the other is 4

-9 times 4 =-36

-9 plus 4 = -5

xy = -36

x= -36/y

x+y =-5

-36/y + y = -5 multiply by y

-36 + y^2 = -5y

y^2 +5y - 36 = 0

factor

(y+9)(y-4) = 0

set each factor = 0

y=-9, y=4

x=4 or x=-9 (x,y) =(4,-9) or (-9,4)

-9(4) =-36

-9+4 = -5

another way to find the two numbers is

graphically.

Graph xy=-36. It's a rectangular hyperbola

graph x+y =-5. It's a line which intersects the hyperbola in two points (4,-9) and (-9,4)