Answer:
5 and -3
Explanation:
You want two integers that have a sum of 2 and a product of -15.
Factor pairs
Solving a problem like this can often be done fairly quickly by listing the factor pairs that make up the product. Only the pairs need be listed that have a sum with the same sign as the sum you're looking for.
Divisors of 15 are 1, 3, 5, and 15. You want a negative product with the largest factor being positive:
-15 = 15(-1) = 5(-3)
The sums of these factor pairs are 14 and 2. The latter pair is the one of interest.
The two integers are 5 and -3.
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Additional comment
The desired relations can be expressed as a quadratic equation. It generally works well to solve it by completing the square.
If one of the numbers is x, the other is 2-x. Their product is -15:
x(2 -x) = -15
2x -x^2 = -15 . . . . . eliminate parentheses
x^2 -2x = 15 . . . . . . make the leading coefficient positive
Complete the square by adding the square of half the x-coefficient
x^2 -2x +1 = 15 +1
(x -1)^2 = 16
x -1 = √16 = 4 . . . . . . take the square root
x = 5 . . . . . . . . . . . add 1
2-x = 2 -5 = -3 . . . . the other number