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Q.
The value of $c (\neq 1)$ for which the equation $x ^2+ x + c =0$ and $x ^2+ cx +1=0$ have one root in common is
Complex Numbers and Quadratic Equations
Solution:
Let $\alpha$ be their common root.
So, $ \alpha^2+\alpha+ c =0$ ....(1)
and $ \alpha^2+ c \alpha+1=0$ ...(2)
Subtracting _________
$(1-c) \alpha+(c-1)=0 \Rightarrow(1-c)(\alpha-1)=0$
But $c \neq 1 \Rightarrow \alpha=1$
$\therefore$ Putting $\alpha=1$ in equation (1), we get $1+1+ c =0$
Hence, $c =-2$.