Question

two negative integers are 5 units apart on the number line, and their product is 126. what is the sum of the two integers? –23 –5 9 14

Answer 1

Answer: A. -23

Explanation:

Answer 2

Answer: Their sum is -23.

Explanation:

Here, the two negative integers are 5 units apart on the number line,

Suppose x is one integer, ( smaller )

Then the other integer is x + 5 ( larger )

Their product = x(x+5),

According to the question,

x(x+5) = 126

⇒
`x^2+5x=126`

⇒
`x^2+5x-126=0`

⇒
`x^2 +14x - 9x - 126=0`

⇒
`x(x+14)-9(x-14)=0`

⇒
`(x-9)(x+14)=0`

If x - 9 = 0 ⇒ x = 9 ( Not a negative integer )

If x + 14 = 0 ⇒ x = -14,

First negative integer = -14,

Second = -14 + 5 = 9

Thus, the required negative integers are -14 and -9.

Now, their sum = -14 - 9 = -23