Question

Product is -8 and sum is 2. What are the two numbers

Answer 1

Step-by-step explanation:

Let the two numbers be x and y.

$\therefore \: xy = - 8...(1) \\ and \\ x + y = 2 \\ \\ \therefore \:x = 2 - y...(2)$

From equations (1) & (2)

$(2-y)y=-8\\\therefore \: 2y - y^2 = - 8\\\\\therefore \:y^2 - 2y-8=0\\\\\therefore \:y^2 - 4y+2y-8=0\\\\\therefore \:y(y - 4)+2(y-4)=0\\\\\therefore \:(y+2)(y - 4)=0\\\\\therefore \:(y+2)=0\:\: or\:\:(y - 4)=0\\\\\therefore \:y=-2\:\: or\:\:y =4\\\\ When \:\: y = - 2\implies x = 4\\\\When \:\: y = 4\implies x = - 2$

Thus, the two numbers are (4, - 2) or (-2, 4).