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# Math

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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?

DragonSlayer554  Aug 26, 2018
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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
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Hi DS it is really good to see you again :)

Melody  Aug 26, 2018
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What Melody said....!!!

CPhill  Aug 26, 2018