2005 AMC 10B Problems/Problem 16

Solution

x^2+mx+n=0 Roots: 2a, 2b 2a + 2b = 2(a+b) = -m 2a • 2b = 4ab = n

x^2+px+m=0 Roots: a, b a + b = -p ab = m

Use substitution:

/frac{n}{p} = /frac{4ab}{-(a+b)} = /frac{8ab}{-2(a+b)} = /frac{8m}{m} = 8

Our answer is 8.

See Also

• 2005 AMC 10B Problems