Difference between revisions of "2005 AMC 10B Problems/Problem 16"
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== Problem == | == Problem == | ||
== Solution == | == 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 == | == See Also == | ||
*[[2005 AMC 10B Problems]] | *[[2005 AMC 10B Problems]] | ||
Revision as of 17:17, 19 January 2010
Problem
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.
