Difference between revisions of "1983 AHSME Problems/Problem 18"
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&= x^4 + x^2 - 3.\end{align*}</cmath> | &= x^4 + x^2 - 3.\end{align*}</cmath> | ||
The answer is therefore <math>\boxed{\textbf{(B)}}</math>. | The answer is therefore <math>\boxed{\textbf{(B)}}</math>. | ||
+ | |||
+ | ==See Also== | ||
+ | {{AHSME box|year=1983|num-b=17|num-a=19}} | ||
+ | |||
+ | {{MAA Notice}} |
Latest revision as of 00:55, 20 February 2019
Problem
Let be a polynomial function such that, for all real , . For all real is
Solution
Let . Then , so we can write the given equation as Then substituting for , we get The answer is therefore .
See Also
1983 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.