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

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(A) Let the common root be $\alpha$. Since $\alpha$ is a root of both equations,we have:$a\alpha^2 + b\alpha + c = 0$  $(1)$$c\alpha^2 + b\alpha + a =

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(A) Let the common root be $\alpha$. Since $\alpha$ is a root of both equations,we have:$a\alpha^2 + b\alpha + c = 0$  $(1)$$c\alpha^2 + b\alpha + a = 0$  $(2)$Subtracting $(2)$ from $(1)$:$(a - c)\alpha^2 + (c - a) = 0$$(a - c)(\alpha^2 - 1) = 0$Since $a 
eq c$,we must have $\alpha^2 - 1 = 0$,which implies $\alpha = 1$ or $\alpha = -1$.Given that the common root is negative,we have $\alpha = -1$.Substituting $\alpha = -1$ into the first equation:$a(-1)^2 + b(-1) + c = 0$$a - b + c = 0$

If the equations $ax^2 + bx + c = 0$ and $cx^2 + bx + a = 0$ $(a \neq c)$ have a common negative root,then the value of $a - b + c$ is:

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