Question

Find two numbers whose product is -48 and whose sum is -8.

Answer 1

$x+y=-8 xy =-48 \implies y= - \frac{48}{x} \implies x - \frac{48}{x} = -8 \implies x^2+8x-48=0 \implies (x+12)(x-4)=0 \implies (x,y)=(-12,4),(4,-12)$