annya2008
18

# what 2 numbers add to get 2 and multiply to 4

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