Final answer:
The two numbers that add up to 5 and multiply to -12 are 3 and -4. To find these numbers, we use the conditions that they must sum to 5 and have a product of -12, and one must be negative while the other is positive.
Step-by-step explanation:
The student is asking to find two numbers that when added equal 5, and when multiplied result in -12. To solve this, we need to find two numbers that meet both conditions. One approach is to guess and check, but a more systematic way is to set up a system of equations based on the given conditions:
- x + y = 5 (They add up to 5)
- xy = -12 (They multiply to -12)
In this case, we're looking for a pair where one number is positive and one is negative, because when the two numbers multiplied have opposite signs, the answer has a -ve sign. We can list pairs of factors of -12 (considering the negative sign):
- (-1, 12)
- (-2, 6)
- (-3, 4)
- (3, -4)
- (2, -6)
- (1, -12)
Now we look for a pair that adds up to 5, which is (3, 2). However, since we need a negative product, the correct pair is (3, -4). So the two numbers are 3 and -4.