Difference between revisions of "2001 SMT/Algebra Problems/Problem 4"
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Any value of <math>p(x)</math> can have at most three solutions due to being at most cubic. But there are four distinct solutions, so <math>p(x)</math> must be a constant function; thus <math>p(0)=p(x)=\boxed{7}</math>. | Any value of <math>p(x)</math> can have at most three solutions due to being at most cubic. But there are four distinct solutions, so <math>p(x)</math> must be a constant function; thus <math>p(0)=p(x)=\boxed{7}</math>. | ||
| − | ~eevee9406 | + | ~ [https://artofproblemsolving.com/wiki/index.php/User:Eevee9406 eevee9406] |
Latest revision as of 20:29, 19 March 2025
Problem
is a real polynomial of degree at most 3. Suppose there are four distinct solutions to the equation = 7. What is 
?
Solution
Any value of can have at most three solutions due to being at most cubic. But there are four distinct solutions, so must be a constant function; thus 
.
