If the equations x^2 + bx + c = 0 and x^2 + c | vedclass

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(C) Let $\alpha$ be the common root of the equations $x^2 + bx + c = 0$ and $x^2 + cx + b = 0$.Then,$\alpha^2 + b\alpha + c = 0$ and $\alpha^2 + c\alp

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$b + c + 1 = 0$

Vedclass · Answer

(C) Let $\alpha$ be the common root of the equations $x^2 + bx + c = 0$ and $x^2 + cx + b = 0$.Then,$\alpha^2 + b\alpha + c = 0$ and $\alpha^2 + c\alpha + b = 0$.Subtracting the two equations: $(\alpha^2 + b\alpha + c) - (\alpha^2 + c\alpha + b) = 0$.This simplifies to $(b - c)\alpha + (c - b) = 0$.$(b - c)\alpha = b - c$.Since $b 
eq c$,we can divide by $(b - c)$ to get $\alpha = 1$.Substituting $\alpha = 1$ into the first equation: $1^2 + b(1) + c = 0$.Therefore,$1 + b + c = 0$,which means $b + c + 1 = 0$.

If the equations $x^2 + bx + c = 0$ and $x^2 + cx + b = 0$ $(b \neq c)$ have a common root,then:

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