Asked by Becky-G
Are there two integers with a product of -12 and a sum of -3?
Answers
Answered by
Reiny
You could go through all the possibilities, after all there are only a limited number of cases, but
let one integer be x and the other one y
x+y = -3
y = -3-x
product = xy = -12
x(-3-x) = -12
-3x - x^2 + 12 = 0
x^2 + 3x - 12 = 0
x = (-3 ± √(9 - 4(1)(-12)) )/2
= (-3 ± √57)/2
which is irrational, so no two integers exist with your stated property
let one integer be x and the other one y
x+y = -3
y = -3-x
product = xy = -12
x(-3-x) = -12
-3x - x^2 + 12 = 0
x^2 + 3x - 12 = 0
x = (-3 ± √(9 - 4(1)(-12)) )/2
= (-3 ± √57)/2
which is irrational, so no two integers exist with your stated property
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