+379 The roots of the equation \(2x^2-mx+n=0\) sum to 6 and multiply to 10. What is the value of \(m+n\)?
+1223 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, \(m+n=12+20 = \boxed{32}\)
+1223 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, \(m+n=12+20 = \boxed{32}\)
