Answer:
-8 and -140
Step-by-step explanation:
Let the numbers be x and y. Then xy = 1120, and x + y = -148.
Solving the first equation for y, we get 1120/x.
Substituting this into the second equation: x + 1120/x = -148
Multiplying all terms by x removes x from the denominator(s):
x² + 1120 + 148x = 0.
Let's use the quadratic formula to find x. Here a = 1, b = 148 and c = 1120.
Then the discriminant is b²-4ac, or, in this case, 148²-4(1)(1120) = 17424. Because this discriminant is positive, we have two real, unequal roots.
They are:
-148 ± √17424
x = ------------------------ = -8 and -140.
2
Note that -8 and -140 add up to -148, so that's correct.
(-8)(-140) = 1120, so that also is correct.
