Question

What 2 numbers add to get 2 and multiply to 4

Answer 1

factor 4
4=1 times 4
2 times 2
they don't add to 2
set up equation
x+y=2
xy=4

first equation, subtract x from both sides
y=2-x
subsitute for y
x(2-x)=4
distribute
2x-x^2=4
add x^2
2x=x^2+4
subtract 2x
0=x^2-2x+4
use quadratic formula which is
if you have ax^2+bx+c=0 then
x=
`\frac{ -b+/-\sqrt{b^(2)-4ac} }{2a}` so

1x^2-2x+4=0
a=1
b=-2
c=4
x=
`\frac{ -(-2)+/-\sqrt{(-2)^(2)-4(1)(4)} }{2(1)}`
x=
`( 2+/-√(4-16) )/(2)`
x=
`( 2+/-√(-12) )/(2)`
we have
`√(-12)` and that doesn't give a real solution
therefor there are no real solutions
but if you want to solve fully
x=
`( 2+/-2√(-3) )/(2)`
i=
`√(-1)`
x=
`( 2+/-2i√(3) )/(2)`
x=
`1+/-i√(3)`
x=
`1-i√(3)` or x=
`1+i√(3)` (those are the 2 numbers)