The sum of two integers is -11 and their product is -80. Find the integers.

1 thought on “The sum of two integers is -11 and their product is -80. Find the integers.”

1. Answer:

   Step-by-step explanation:

   Let two integers be x and y

   Sum of x and y, x+y = -11 ———–(1)

   Their Product, xy = -80

   y = -80 / x ————–(2)

   Put eq (2) in eq(1),

   x + (-80 / x) = -11

   [tex]x^{2} -80[/tex] = -11x

   [tex]x^{2} + 11x -80 = 0[/tex]

   x=−b±b2−4ac/√2a

   x=−11±112−4(1)(−80)/√2(1)

   x=−11±121−−320/2

   x=−11±441/√2

   The discriminant b2−4ac>0

   so, there are two real roots.

   Simplify the Radical:

   x=−11±212

   x=102x=−322

   which becomes

   x=5

   x=−16

   now put x in eq (2)

   when x = 5,

   y=-80/5 = -16

   when x=-16

   y=-80/-16 = 5

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