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Difference between revisions of "1977 AHSME Problems/Problem 21"

(Created page with "== Problem 21 == For how many values of the coefficient a do the equations <cmath>\begin{align*}x^2+ax+1=0 \\ x^2-x-a=0\end{align*}</cmath> have a common real solution? <mat...")
 
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\textbf{(C)}\ 2 \qquad
 
\textbf{(C)}\ 2 \qquad
 
\textbf{(D)}\ 3 \qquad
 
\textbf{(D)}\ 3 \qquad
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\textbf{(E)}\ \infty</math>   
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\textbf{(E)}\ \infty</math>
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==Solution==
 
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Solution by e_power_pi_times_i
 
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The solutions to the equations are <math>\dfrac{-a\pm\sqrt{a^2-4}}{2}</math> and <math>\dfrac{1\pm}{}</math>
 

Revision as of 12:27, 22 November 2016

Problem 21

For how many values of the coefficient a do the equations \begin{align*}x^2+ax+1=0 \\ x^2-x-a=0\end{align*} have a common real solution?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ \infty$

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