The sum of two numbers is 12. The product of those same two numbers is -64. Find the numbers.

Answer 1

Let the two numbers be x and y

Then x+y=12 and xy=-64

Solve the first equation for y

x+y=12

y=12-x

Substitute into the second equation and solve for x

xy=-64

x(12-x)=-64

12x-x²=-64

0=x²-12x-64

0=(x+4)(x-16)

Then x=-4 or x=16

So, the two numbers are -4 and 16