Question

find the pair of integers whose product is the first integer and whose sum is the second integer -40,-6

Answer 1

$x;y-the\ integers\\\\ \left\{\begin{array}{ccc}xy=-40&(1)\\x+y=-6&\to x=-6-y&(2)\end{array}\right\\\\subtitute\ (2)\ to\ (1):\\\\(-6-y)(y)=-40\\(-6)(y)+(-y)(y)=-40\\-6y-y^2=-40\\-y^2-6y+40=0\ \ \ \ |change\ the\ signs\\y^2+6y-40=0\\y^2+10y-4y-40=0\\y(y+10)-4(y+10)=0\\(y+10)(y-4)=0\iff y+10=0\ or\ y-4=0\\\boxed{y=-10\ or\ y=4}$

$subtitute\ the\ values\ of\ "y"\ to\ (2):\\x=-6-(-10)=-6+10\to\boxed{x=4}\\or\\x=-6-4\to\boxed{x=-10}\\\\Answer{\boxed{\boxed{4\ and\ -10}}$