If a root of the equations x^2 + px + q = 0 a | vedclass

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(C) Let the common root be $y$. Then,$y^2 + py + q = 0$ and $y^2 + \alpha y + \beta = 0$. Subtracting the two equations: $(y^2 + py + q) - (y^2 + \alp

Vedclass · Accepted Answer

$\frac{q - \beta}{\alpha - p}$ or $\frac{p\beta - \alpha q}{q - \beta}$

Vedclass · Answer

(C) Let the common root be $y$. Then,$y^2 + py + q = 0$ and $y^2 + \alpha y + \beta = 0$. Subtracting the two equations: $(y^2 + py + q) - (y^2 + \alpha y + \beta) = 0$ $y(p - \alpha) + (q - \beta) = 0$ $y(p - \alpha) = \beta - q$ $y = \frac{\beta - q}{p - \alpha} = \frac{q - \beta}{\alpha - p}$. Alternatively,using the method of cross-multiplication for the system: $\frac{y^2}{p\beta - q\alpha} = \frac{y}{q - \beta} = \frac{1}{\alpha - p}$. From the second and third terms,$y = \frac{q - \beta}{\alpha - p}$. From the first and second terms,$y = \frac{p\beta - q\alpha}{q - \beta}$. Thus,the common root is $\frac{q - \beta}{\alpha - p}$ or $\frac{p\beta - \alpha q}{q - \beta}$.

If a root of the equations $x^2 + px + q = 0$ and $x^2 + \alpha x + \beta = 0$ is common,then its value will be (where $p \neq \alpha$ and $q \neq \beta$)

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