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# I need help, thanks in advance.

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The roots of the equation $$2x^2-mx+n=0$$ sum to 6 and multiply to 10. What is the value of $$m+n$$?

Feb 20, 2021

#1
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We can use Vieta's Formulas. The sum of the roots is $$-\frac{b}{a} = \frac{m}{2}$$ and the product of the roots is $$\frac{c}{a} = \frac{n}{2}$$.

The sum is 6, so $$\frac{m}{2}=6$$ and m = 12.

The product is 10, so $$\frac{n}{a} = 10$$ and n = 20.

So, $$m+n=12+20 = \boxed{32}$$

Feb 20, 2021

#1
+944
+3

We can use Vieta's Formulas. The sum of the roots is $$-\frac{b}{a} = \frac{m}{2}$$ and the product of the roots is $$\frac{c}{a} = \frac{n}{2}$$.

The sum is 6, so $$\frac{m}{2}=6$$ and m = 12.

The product is 10, so $$\frac{n}{a} = 10$$ and n = 20.

So, $$m+n=12+20 = \boxed{32}$$

CubeyThePenguin Feb 20, 2021
#2
+294
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Thank you!

calvinbun  Feb 20, 2021