If the equations x^2 + px + q = 0 and x^2 + q | vedclass

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(A) Let $\alpha$ be the common root of the two equations.Then,$\alpha^2 + p\alpha + q = 0$ $(i)$And $\alpha^2 + q\alpha + p = 0$ $(ii)$Subtracting equ

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(A) Let $\alpha$ be the common root of the two equations.Then,$\alpha^2 + p\alpha + q = 0$ $(i)$And $\alpha^2 + q\alpha + p = 0$ $(ii)$Subtracting equation $(ii)$ from equation $(i)$:$(\alpha^2 + p\alpha + q) - (\alpha^2 + q\alpha + p) = 0$$(p - q)\alpha + (q - p) = 0$$(p - q)\alpha - (p - q) = 0$$(p - q)(\alpha - 1) = 0$Assuming $p 
eq q$,we get $\alpha = 1$.Substituting $\alpha = 1$ into equation $(i)$:$1^2 + p(1) + q = 0$$1 + p + q = 0$Therefore,$p + q + 1 = 0$.

If the equations $x^2 + px + q = 0$ and $x^2 + qx + p = 0$ have a common root,then $p + q + 1 = $

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