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- Feb 5, 2012

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**srirahulan's question titled "Algeb" from Math Help Forum,**

Hi srirahulan,If \(ax^2+2x+1=0\mbox{ and }x^2+2x+a=0\) have the common roots, find the real value of a.

Let \(\alpha\mbox{ and }\beta\) be the two roots of these quadratic equations. Then, according to the first equation,

\[\alpha+\beta=-\frac{2}{a}~~~~~~(1)\]

Considering the second equation,

\[\alpha+\beta=-2~~~~~~~(2)\]

By (1) and (2);

\[-\frac{2}{a}=-2\]

\[\therefore a=1\]