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Are there two integers with a product of -12 and a sum of -3? Explain.

 

I said no, but how do I explain?

 Aug 26, 2018
 #1
avatar+391 
+4

We have two integers, \(x\) and \(y\).

 

\(x*y = -12\)

\(x + y = -3\)

 

\(y = -3-x\)

 

\(x*(-3-x) = -12\)

 

\(-x^2 - 3x + 12 = 0\)

 

Now, we can use the quadratic formula to find the two factors: \(\frac{-b ± \sqrt{b^2 - 4ac}}{2a}\).

 

\(\frac{3 ± \sqrt{57}}{-2}\), so the two roots are \(\frac{3 - \sqrt{57}}{-2}\) and \(\frac{3 + \sqrt{57}}{-2}\). These two numbers are the only numbers that have a product of \(-12\) and a sum of \(-3\), BUT, they are NOT integers.

 

- Daisy

 Aug 26, 2018
 #2
avatar+101054 
+3

Hi DS it is really good to see you again :)

 Aug 26, 2018
 #3
avatar+100587 
+2

What Melody said....!!!

 

cool cool cool

CPhill  Aug 26, 2018

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