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# If the equations $x^2+bx+c=0$ and $x^2+cx+b=0$ have one common root, then

(A) $b+c=0$

(B) $b+c=1$

(C) $b+c=-1$

(D) $b-c=1$

Can you answer this question?

Given: $x^2+bx+c=0$ and $x^2+cx+b=0$
have one root common.
Let $\alpha$ be the common root.
$\therefore\:\alpha^2+b\alpha+c=0$ and $\alpha^2+c\alpha+b=0$
Subtracting these two equations we get $\alpha=1$
$\therefore\:1+b+c=0$
$\Rightarrow\:b+c=-1$
answered Jul 27, 2013