If alpha and beta are the roots of the equati | vedclass

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(D) Given that $\alpha$ and $\beta$ are roots of $ax^2 + bx + c = 0$,we have $\alpha + \beta = -\frac{b}{a}$ and $\alpha\beta = \frac{c}{a}$.We need t

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$-\frac{2}{a}$

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(D) Given that $\alpha$ and $\beta$ are roots of $ax^2 + bx + c = 0$,we have $\alpha + \beta = -\frac{b}{a}$ and $\alpha\beta = \frac{c}{a}$.We need to evaluate the expression $E = \frac{\alpha}{a\beta + b} + \frac{\beta}{a\alpha + b}$.Since $a\alpha^2 + b\alpha + c = 0$,we have $a\alpha + b = -\frac{c}{\alpha}$. Similarly,$a\beta + b = -\frac{c}{\beta}$.Substituting these into the expression:$E = \frac{\alpha}{-c/\beta} + \frac{\beta}{-c/\alpha} = -\frac{\alpha\beta}{c} - \frac{\beta\alpha}{c} = -\frac{2\alpha\beta}{c}$.Substituting $\alpha\beta = \frac{c}{a}$:$E = -\frac{2(c/a)}{c} = -\frac{2}{a}$.

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$,then $\frac{\alpha}{a\beta + b} + \frac{\beta}{a\alpha + b} = $

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