Difference between revisions of "2005 AMC 10B Problems/Problem 16"

 
(Solution)
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== Problem ==
 
== Problem ==
 
== Solution ==
 
== Solution ==
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 +
x^2+mx+n=0
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Roots: 2a, 2b
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2a + 2b = 2(a+b) = -m
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2a • 2b = 4ab = n
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x^2+px+m=0
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Roots: a, b
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a + b = -p
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ab = m
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Use substitution:
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/frac{n}{p}
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= /frac{4ab}{-(a+b)}
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= /frac{8ab}{-2(a+b)}
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= /frac{8m}{m}
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= 8
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 +
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.

See Also

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