Question

the sum of two integers is-11 and their product is-80 what are the two integers?​

Answer 1

Answer:

The two integers are - 16 & 5.

Step-by-step-explanation:

Let the first integer be x.

And the other integer be y.

From the first condition,

x + y = - 11

⇒ x = - 11 - y - - - - - - - ( 1 )

From the second condition,

xy = - 80

⇒ ( - 11 - y ) * y = - 80 - - - - [ From ( 1 ) ]

⇒ - 11y - y² = - 80

⇒ - 80 + 11y + y² = 0

⇒ y² + 11y - 80 = 0

⇒ y² + 16y - 5y - 80 =x = - 11 - y 0

⇒ y ( y + 16 ) - 5 ( y + 16 ) = 0

⇒ ( y + 16 ) ( y - 5 ) = 0

⇒ ( y + 16 ) = 0 OR ( y - 5 ) = 0

⇒ y + 16 = 0 OR y - 5 = 0

⇒ y = - 16 OR y = 5

Now, by substituting y = - 16 in equation ( 1 ),

x = - 11 - y

⇒ x = - 11 - ( - 16 )

⇒ x = - 11 + 16

⇒ x = 5

By substituting y = 5 in equation ( 1 ),

x = - 11 - y

⇒ x = - 11 - 5

⇒ x = - 16

∴ The two integers are - 16 & 5.