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2008 AMC 10B Problems/Problem 9

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Problem

A quadratic equation ax^2 - 2ax + b = 0 has two real solutions. What is the average of these two solutions?

\mathrm{(A)}\ 1\qquad\mathrm{(B)}\ 2\qquad\mathrm{(C)}\ \frac ba\qquad\mathrm{(D)}\ \frac{2b}a\qquad\mathrm{(E)}\ \sqrt{2b-a}

Solution

Dividing both sides by a, we get x^2 - 2x + b/a = 0. By Vieta's formulas, the sum of the roots is 2, therefore their average is 1\Rightarrow \boxed{A}.

See also

2008 AMC 10B (Problems • Resources)
Preceded by
Problem 8 		Followed by
Problem 10
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
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