What adds to get 2 and multiplies to get -4?

Answer 1

To solve this, you can set up a system of equations, with "x" representing one number and "y" representing another number. From the given conditions, you can set up a system of at most two equations. With this system you can solve for no more than two variables. So, from this you can only find pair(s) of numbers that satisfy these conditions, as opposed to sets of three or four numbers that do this. From the conditions:

x + y = 2

xy = -4

Using the second equation, solve for y and substitute this into the first equation:

y = -4/x

x - 4/x = 2

(x2-4)/x = 2

x2-4 = 2x

x2-2x-4 = 0

this is not factorable, so the quadratic equations must be used:

x = (-b +/- sqrt(b2-4ac))/2a

x = (2 +/- sqrt((-2)2-4(1)(-4)))/2(1)

x = (2 +/- sqrt(4+16))/2

x = (2 +/- sqrt(20))/2

x = (2 +/- 2sqrt(5))/2

x= 1 + sqrt(5) and x = 1 - sqrt(5)

So the two numbers that satisfy these conditions are:

1 + sqrt(5)

and

1 - sqrt(5)