Answer: Their sum is -23.
Step-by-step 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
⇒ [tex]x^2+5x=126[/tex]
⇒ [tex]x^2+5x-126=0[/tex]
⇒ [tex]x^2 +14x - 9x - 126=0[/tex]
⇒ [tex]x(x+14)-9(x-14)=0[/tex]
⇒ [tex](x-9)(x+14)=0[/tex]
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
