2022 AIME I Problems/Problem 1
Contents
Problem
Quadratic polynomials and have leading coefficients and respectively. The graphs of both polynomials pass through the two points and Find
Solution 1 (Linear Polynomials)
Let Since the -terms of and cancel, we conclude that is a linear polynomial.
Note that so the slope of is
It follows that the equation of is for some constant and we wish to find
We substitute into this equation to get from which
~MRENTHUSIASM
Solution 2 (Quadratic Polynomials)
Let for some constants and
We are given that and we wish to find We need to cancel and Since we subtract from to get ~MRENTHUSIASM
Video Solution (Mathematical Dexterity)
https://www.youtube.com/watch?v=sUfbEBCQ6RY
See Also
2022 AIME I (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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All AIME Problems and Solutions |
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