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The value of $b$ for which the eqns., $x^2+bx-1=0,\:x^2+x+b=0$ have one common root is

$\begin{array}{1 1} \sqrt 2 \\ - \sqrt 2 \\ \sqrt{3 i} \\ \sqrt {5 i} \end{array} $

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Given: $x^2+bx-1=0\:and\:x^2+x+b=0$ have one common root.
Let the common root be $\alpha$
$\Rightarrow\:\alpha^2+b\alpha-1=0 \: and\:\alpha^2+\alpha+b=0$
$\Rightarrow\:b^2=-3$ or $b=\sqrt 3i$
answered Aug 5, 2013 by rvidyagovindarajan_1

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