Question

Two factors of –48 have a difference of 19. The factor with a greater absolute value is positive.

What is the sum of the factors?

–19
–13
13
16

Answer 1

Let the positive factor be p and the negative factor be n. Since the positive factor has the greater absolute value and their difference is 19, p − n = 19. Also pn = −48.

So p(p − 19) = −48 → p^2 − 19p + 48 = 0.
Solve: p = (19 ± 13)/2 → p = 16 or 3. Only p = 16 gives the positive factor the larger absolute value, giving n = −3.

Sum = 16 + (−3) = 13.