The roots of the equation $2x^2-mx+n=0$ sum to 6 and multiply to 10. What is the value of $m+n$?
To solve this problem, I will use the fact that for any quadratic equation of the form $ax^2+bx+c=0$, the sum of the roots is $-b/a$ and the product of the roots is $c/a$. In this case, the equation is $2x^2-mx+n=0$, so $a=2$, $b=-m$, and $c=n$. Therefore, the sum of the roots is $-(-m)/2=m/2$ and the product of the roots is $n/2$. But the problem also tells me that the sum of the roots is 6 and the product of the roots is 10. So I can set up two equations: $m/2=6$ and $n/2=10$. Solving for $m$ and $n$, I get $m=12$ and $n=20$. The problem asks for the value of $m+n$, so I just need to add them up. I get $m+n=12+20=32$. 