2007 AMC 12A Problems/Problem 18
Problem
The polynomial 
has real coefficients, and 
What is 
Solution
A fourth degree polynomial has four roots. Since the coefficients are real(meaning that complex roots come in conjugate pairs), the remaining two roots must be the complex conjugates of the two given roots, namely 
. Now we work backwards for the polynomial:
Thus our answer is 
.
See also
| 2007 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 17 |
Followed by Problem 19 |
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| All AMC 12 Problems and Solutions | |
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