Question

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

Answer 1

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\\</p><p>\therefore \: 2y - y^2 = - 8\\\\</p><p>\therefore \:y^2 - 2y-8=0\\\\</p><p>\therefore \:y^2 - 4y+2y-8=0\\\\</p><p>\therefore \:y(y - 4)+2(y-4)=0\\\\</p><p>\therefore \:(y+2)(y - 4)=0\\\\</p><p>\therefore \:(y+2)=0\:\: or\:\:(y - 4)=0\\\\</p><p>\therefore \:y=-2\:\: or\:\:y =4\\\\ </p><p>When \:\: y = - 2\implies x = 4\\\\</p><p>When \:\: y = 4\implies x = - 2\\</p><p>`

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