Difference between revisions of "1999 AHSME Problems/Problem 12"
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==Problem== | ==Problem== | ||
| − | What is the maximum number of points of intersection of the graphs of two different fourth degree polynomial functions <math> y | + | What is the maximum number of points of intersection of the graphs of two different fourth degree polynomial functions <math> y=p(x)</math> and <math> y=q(x)</math>, each with leading coefficient 1? |
<math> \textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 8</math> | <math> \textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 8</math> | ||
Revision as of 09:37, 4 December 2015
Problem
What is the maximum number of points of intersection of the graphs of two different fourth degree polynomial functions 
and 
, each with leading coefficient 1?
Solution
Since the two graphs are fourth degree polynomials, then they can have at most 
intersections, giving the answer of 
.
See Also
| 1999 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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. 
