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 18:35, 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) | |
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