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 \equal{} p(x)</math> and <math> y \equal{} q(x)</math>, each with leading coefficient 1?
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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 $y=p(x)$ and $y=q(x)$, 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
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