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
 

Attachments

  • 036.png
    036.png
    3.3 KB · Views: 122
Mathematics news on Phys.org
  • #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:

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

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.

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.

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).

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.

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.

Similar threads

MHB How do you factor expressions like 3(x + h)^4 - 48(x + h)^2?
Replies
2
Views
1K
MHB Finding roots of a quadratic (Lindsay's question from Facebook)
Replies
0
Views
2K
MHB Solving for x and k: Positive Ints
Replies
12
Views
3K
A Finite series and product of Gammas
Replies
8
Views
1K
I Can New Theorems Predict Incomplete 5x5 Magic Square Solutions?
2
Replies
68
Views
10K
MHB How Do You Solve a Geometric Sum with Alternating Signs?
Replies
2
Views
1K
Summing divergences and the real projective line
Replies
4
Views
2K
B Natural Numbers contain all the Primes
Replies
24
Views
2K
MHB Prove: Positive Integer n Sum Equation
Replies
3
Views
2K
MHB Find Vol Bound by $x_2 =\frac{y+1}{2}$ & $x_1=y^2$
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top