2002 AMC 10P Problems/Problem 11: Difference between revisions
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[[Category: Intermediate Algebra Problems]] | |||
Latest revision as of 20:43, 15 October 2025
Problem
Let 
Find the sum of all real numbers 
for which 
is a factor of 
Solution 1
By the factor theorem, is a factor of 
if and only if 
Therefore, 
must equal 
which simplifies to 
is a trivial real 
. Since 
this polynomial does indeed have two real zeros, meaning we can use Vieta’s to conclude that sum of the other two roots are 
Thus, our answer is 
See also
| 2002 AMC 10P (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
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