What two numbers add to be -3 and multiply to be -4?

Answer 1

-7

Answer 2

1 & -4

You have two equations:

x+y = -3

x*y = -4

and two unknowns (x & y), so this is solvable. One way, is to solve for y in the 1st equation,

x+y = -3 ===> y = -3 - x

and plug it into the 2nd:

-4 = x*y = x*(-3 - x) = -3x - x2

==> x2 + 3x - 4 = 0

Then use the quadratic formula to solve for x:

x = 1/2 * ( -3 +- Sqrt( 32 - 4*(-4) ) )

= 1/2 * ( -3 +- Sqrt( 9 + 16 ) ) = 1/2 * ( -3 +- 5 )

= (for positive root) 1/2 * 2 = 1

= (for negative root) 1/2 * -8 = -4

So x can be either 1 or -4 (and y = -3-x will be -4 or 1). Yay math!