Question

write a pair of integer in which multiplication is -40 find difference is 12​

Answer 1

Given :  a pair of integer in which multiplication is -40 and difference is 12

To Find : pair of integer

Solution:

difference is 12

Hence let say integers are a  and a + 12

multiplication is - 40

=> a(a + 12) = -40

=> a²  + 12a   + 40 = 0

=> D = √12² - (4)(40)    = √-16  

Hence no real roots exist for this

so no pair of integer exists satisfying given condition

if difference is 14

Then  a²  + 14a   + 40 = 0

=> (a + 10)(a + 4) = 0

=> a = - 10  and a = - 4

a + 14 = 4  and  10

hence pair of integers ( - 10 , 4) and ( - 4 , 10)

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Answer 2

Correct Question :- write a pair of integer in which multiplication is -40 find difference is 14 ?

Solution :-

Let us assume that, one integer is x .

so,

• second integer = (x + 14) .

given that,

→ Product = (-40)

→ x * (x + 14) = (-40)

→ x² + 14x = (-40)

→ x² + 14x + 40 = 0

→ x² + 10x + 4x + 40 = 0

→ x(x + 10) + 4(x + 10) = 0

→ (x + 10)(x + 4) = 0

→ x = (-10) or (-4) .

then,

• if x = (-10) => other number = (-10) + 14 = 4 .
• if x = (-4) => other number = (-4) + 14 = 10 .

Hence, required pair of integer are (-10,4) and (-4,10) .

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