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  4. If the quadratic equations x2+k x+1=0 and x2+x+k=0 have a common root, then sum of possible value(s) of k is

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Q. If the quadratic equations $x^2+k x+1=0$ and $x^2+x+k=0$ have a common root, then sum of possible value(s) of $k$ is

Complex Numbers and Quadratic Equations

Solution:

$x ^2+ kx +1=0$
$x ^2+ x + k =0$
$( k -1) x =( k -1) $
$\Rightarrow k =1 \text { or } x =1 \Rightarrow 1+ k +1=0 \Rightarrow k =-2$
$k =1 \Rightarrow$ both roots are common.