2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4
Problem
Find a second-degree polynomial with integer coefficients, , such that , and are perfect squares, but is not.
Solution
Answer: A polynomial that satisfies the criteria is easily constructed by first centering it at , that is . Now we have two conditions: and that determines possible candidates that can then be checked against the condition that is not a perfect square and the condition that the coefficients are integers. A few possible answers are
See also
2017 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNM-PNM Problems and Solutions |