2022 AIME I Problems/Problem 1
Revision as of 16:50, 17 February 2022 by MRENTHUSIASM (talk | contribs)
Contents
Problem 1
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 the graph of passes through
and
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
See Also
2022 AIME I (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.