Common roots and finding real values

[Sudharaka]

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

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

Hi srirahulan,

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);

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

\[\therefore a=1\]

 

[fresh_42]

Correct. An explanation of equation (1) would have been nice.
https://en.wikipedia.org/wiki/Vieta's_formulas