Difference between revisions of "2002 AMC 12A Problems/Problem 25"
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==Solution== | ==Solution== | ||
| − | + | The sum of the coefficients of <math>P</math> and of <math>Q</math> will be equal, so <math>P(1) = Q(1)</math>. The only answer choice with an intersection between the two graphs at <math>x = 1</math> is <math>(B)</math>. (The polynomials in the graph are <math>P(x) = 2x^4-3x^2-3x-4</math> and <math>Q(x) = -2x^4-2x^2-2x-2</math>.) | |
==See Also== | ==See Also== | ||
Revision as of 17:35, 7 April 2014
Problem
The nonzero coefficients of a polynomial 
with real coefficients are all replaced by their mean to form a polynomial 
. Which of the following could be a graph of 
and 
over the interval 
?
Solution
The sum of the coefficients of and of will be equal, so 
. The only answer choice with an intersection between the two graphs at 
is 
. (The polynomials in the graph are 
and 
.)
See Also
| 2002 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 24 |
Followed by Last Problem |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
