What are the factors of -48 that result in a positive sum?

In summary, the product of two integers is -48 when their sum is a positive number. The sum of two integers can be positive when their product is -48, and some possible combinations include (-6, 8), (-8, 6), (-12, 4), (-4, 12), (-24, 2), and (-2, 24). However, it is not possible for one of the integers to be 0 in this scenario. To solve for the two integers, a system of equations can be set up and solved by using algebraic manipulation. The possible solutions are (±√48, y) where y is any number greater than ±√48.
  • #1
karush
Gold Member
MHB
3,269
5
ok I don't don't know de jure on this so ...

is it just plug and play??

find factors of -48
$-1(48)=-48$
$-2(24)=-48$
$-3(16)=-48$
$-4(12)=-48$
$-6(8)=-48$
check sums for positive number
$-1+48=47$
$-2+24=22$
$-3+16=13$
$-4+12=8$
$-6+8=2$it looks like c. 5
 

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  • #2
karush said:
is it just plug and play??

Well, if just plug and play can get you there faster, why bother with theoretical method?
 
  • #3
mahalo;)
 
Last edited:

1. What is the product of two integers if their sum is positive and their product is -48?

The product of two integers is -48 if their sum is positive. This means that the two integers must be negative, as a positive multiplied by a negative would result in a negative product.

2. Can the sum of two integers be positive if their product is -48?

Yes, the sum of two integers can be positive if their product is -48. This is because the two integers could be negative, resulting in a positive sum.

3. What are the possible pairs of integers that could have a product of -48 and a positive sum?

The possible pairs of integers that could have a product of -48 and a positive sum are (-8, 6), (-6, 8), (-4, 12), (-12, 4), (-3, 16), (-16, 3), (-2, 24), (-24, 2), (-1, 48), and (-48, 1).

4. How can you determine the two integers if their product is -48 and their sum is positive?

To determine the two integers, you can use algebraic equations. Let the two integers be represented by x and y. Then, you can set up the equations x + y = a (where a is a positive number) and xy = -48. From there, you can solve for x and y using algebraic methods.

5. Is it possible for the product of two integers to be -48 and their sum to be positive?

Yes, it is possible for the product of two integers to be -48 and their sum to be positive. As mentioned before, the two integers would have to be negative in order for this to be possible.

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