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1977 AHSME Problems/Problem 21

Revision as of 13:17, 22 November 2016 by E power pi times i (talk | contribs) (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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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?

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


Solution

Solution by e_power_pi_times_i


The solutions to the equations are $\dfrac{-a\pm\sqrt{a^2-4}}{2}$ and $\dfrac{1\pm}{}$

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