2005 AMC 12B Problems/Problem 12
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Problem
The quadratic equation 
has roots twice those of 
, and none of 
and 
is zero. What is the value of 
?
Solution
Let 
have roots 
and 
. Then
so 
and 
. Also, 
has roots 
and 
, so
and 
and 
. Thus 
.
Indeed, consider the quadratics 
. See Vieta's formulas.
See also
| 2005 AMC 12B (Problems • Resources) | ||
| Preceded by Problem 11 | Followed by Problem 13 | |
| 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 | ||
