SOLUTION: what 2 numbers add to get -4 and multiply to get 3

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Question 1203982: what 2 numbers add to get -4 and multiply to get 3

Found 3 solutions by MathLover1, MathTherapy, josgarithmetic:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let two numbers be x and y
if 2 numbers add to get -4, we have
x%2By=-4...eq.1

and if multiply to get 3, we have

x%2Ay=3...eq.2... solve for y
y=3%2Fx..eq.2a

substitute in eq.1

x%2B3%2Fx=-4...eq.1.. solve for x, both sides multiply by x
x%5E2%2B3=-4x
x%5E2%2B4x%2B3=0...factor
%28x+%2B+1%29+%28x+%2B+3%29+=+0

solutions:
x=-1
or
x=-3

go to
y=3%2Fx..eq.2a, substitute x
y=3%2F-1=-3
or
y=3%2F-3=-1


so, solutions are
x=-1, y=-3
or
x=-3, y=-1



Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
what 2 numbers add to get -4 and multiply to get 3

Creating equations to answer this is TOTALLY, TOTALLY UNNECESSARY. That's because one just needs to determine
which 2 INTEGERS have a PRODUCT of 3 (+ 3), and sum to - 4. If equations are created, it's the same thing the 
person has to do - if solving using the FACTORING method - unless of course, the person plans on using the
quadratic equation formula, which in this case, in my opinion, is TOTALLY, TOTALLY UNNECESSARY!! 

So, going back to the problem, 3 is PRIME, and so, its ONLY factors are 3 and 1. But, since (+ 3)(+ 1) = + 3, 
and also (- 3)(- 1) = + 3, it's clear that ONLY the factors, - 3 and - 1 SUM to - 4.

Therefore, the 2 integers being sought are  - 3 and - 1.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply to result in 3:
-1 & -3
1 & 3

Add the two numbers to result in -4:
Only ONE of those simple choices works.
-1 and -3.

---
If desired:
two numbers x and -4-x.
x%28-4-x%29=3
-x%5E2-4x=3
-x%5E2-4x-3=0
x%5E2%2B4x%2B3=0
%28x%2B1%29%28x%2B3%29=0
system%28x=-1%2Cor%2Cx=-3%29
.
.
but the two numbers will be -1 and -3.