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

I said no, but how do I explain?

DragonSlayer554
Aug 26, 2018

#1**+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

dierdurst
Aug 26, 2018