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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

Best Answer 

 #1
avatar+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, \(m+n=12+20 = \boxed{32}\)

 Feb 20, 2021
 #1
avatar+944 
+3
Best Answer

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
avatar+294 
+4

Thank you!

calvinbun  Feb 20, 2021

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