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

Let the smaller integer be x. Then the other is x+5 and x(x+5)=126 → x^2+5x-126=0. Solve: x = (-5 ± 23)/2 → x = -14 or 9. Since both are negative, x = -14 and the other is -9. Sum = -23.