Difference between revisions of "1999 AHSME Problems/Problem 12"

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==Solution==
 
==Solution==
  
Finding the number of solutions to <math>p(x) = q(x)</math> will find the number of intersections of the two graphs.
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Since the two graphs are fourth degree polynomials, then they can have at most <math>4</math> intersections, giving the answer of <math>\boxed{D}</math>.
 
 
 
 
Since the two graphs are fourth degree polynomials, then, by they can have at most <math>4</math> intersections (real  solutions), leading to an answer of <math>\boxed{D}</math>.
 
  
 
==See Also==
 
==See Also==

Revision as of 20:37, 13 January 2015

Problem

What is the maximum number of points of intersection of the graphs of two different fourth degree polynomial functions $y \equal{} p(x)$ (Error compiling LaTeX. Unknown error_msg) and $y \equal{} q(x)$ (Error compiling LaTeX. Unknown error_msg), each with leading coefficient 1?

$\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 8$

Solution

Since the two graphs are fourth degree polynomials, then they can have at most $4$ intersections, giving the answer of $\boxed{D}$.

See Also

1999 AHSME (ProblemsAnswer KeyResources)
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
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