If the sum of two integers is –2 and their product is –24, the numbers are

Let, the two integers = x and y

According to problem,

⇒ x + y = - 2 ……… (1)

and

⇒ xy = - 24 ……… (2)

∴ (x + y)² = (-2)²

⇒ (x – y)² + 4xy = 4

⇒ (x – y)² + 4 × (-24) = 4

⇒ (x – y)² = 4 + 96 = 100

⇒ x – y = ±10

Case 1.

x - y = 10 …… (a) and x + y = - 2 …… (b)

From (a) + (b) we get,

⇒ 2x = 8

⇒ x = 4

∴ 4 – y = 10 [from (a)]

⇒ y = 4 – 10

⇒ y = - 6

Case 2.

x – y = - 10 …… (c) and x + y = - 2 …… (d)

From (c) + (d) we get,

⇒ 2x = - 12

⇒ x = - 6

∴ -6 – y = - 10

⇒ y = 10 – 6

⇒ y = 4

∴ The numbers are 4 and – 6.