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?

Answer 1

lets say that y is biggerr
y-x=5
and
y=x+5

pproduct is 126
xy=126
substiutute x+5 for y
(x+5)(x)=126
x^2+5x=126
x^2+5x-126=0
factor
whaat 2 numbbers multtiply to get -126 aand addd to gget 5
-9 and 14
(x-9)(x+14)=0
sset to zzero
x-9=0
x=9, nah we nneed 2 nnegative nnumbers

x+14=0
x=-14

so thenn
y=x+5
y=-14+5
y=-9

the summ is -14-9=-23

Answer 2

If b>a, b-a=5 so b=5+a

ab=126, using b from above

a(5+a)=126

5a+a^2=126

a^2+5a-126=0
 
(a+14)(a-9)=0, since a<0 the numbers are

-14 and -9