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2002 AMC 10B Problems/Problem 10

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Problem

Suppose that $a$ and $b$ are nonzero real numbers, and that the equation $x^2+ax+b=0$ has positive solutions $a$ and $b$ . Then the pair $(a,b)$ is

$\mathrm{(A) \ } (-2,1)\qquad \mathrm{(B) \ } (-1,2)\qquad \mathrm{(C) \ } (1,-2)\qquad \mathrm{(D) \ } (2,-1)\qquad \mathrm{(...$

Solution

From Vieta's Formulas, $ab=b$ and $a+b=-a$ . Since $b\ne 0$ , we have $a=1$ , and hence $b=-2$ . Our answer is $\boxed{(1,-2)\Rightarrow\text{(C)}}$ .

See Also

2002 AMC 10B (Problems • Resources)
Preceded by Problem 9	Followed by Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/2002_AMC_10B_Problems/Problem_10"

Category: Introductory Algebra Problems

Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.

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