Question

The product of two consecutive negative integers is 1122. What are the numbers? The product of two consecutive negative integers is 1122. What are the numbers? @Mathematics

Answer 1

let the first negative integer = x
then consecutive negative integer = x+1

x (x+1) = 1122
x^2 + x = 1122
x^2 + x - 1122 = 0
x^2 + 34x - 33x - 1122 = 0
x(x + 34) -33 (x + 34) = 0
(x - 33)(x + 34) = 0
if x - 33 = 0 then x = 33
if x + 34 = 0 then x = -34

since we negative integer, x = -34 is the acceptable value
so first negative integer = x = -34
consecutive negative integer = x+1 = -34 +1 = -33

so the two negative integers are -34 and -33