If the roots of the equation ax^2 + bx + c = | vedclass

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(A) Given the quadratic equation $ax^2 + bx + c = 0$ with roots $\alpha$ and $\beta$,we have:$\alpha + \beta = -\frac{b}{a}$ and $\alpha\beta = \frac{

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$\frac{c(a - b)}{a^2}$

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(A) Given the quadratic equation $ax^2 + bx + c = 0$ with roots $\alpha$ and $\beta$,we have:$\alpha + \beta = -\frac{b}{a}$ and $\alpha\beta = \frac{c}{a}$.We need to find the value of $\alpha\beta^2 + \alpha^2\beta + \alpha\beta$.Factoring out $\alpha\beta$,we get:$\alpha\beta(\beta + \alpha) + \alpha\beta = \alpha\beta(\alpha + \beta + 1)$.Substituting the values of $\alpha + \beta$ and $\alpha\beta$:$= \frac{c}{a} \left( -\frac{b}{a} + 1 \right)$$= \frac{c}{a} \left( \frac{a - b}{a} \right)$$= \frac{c(a - b)}{a^2}$.

If the roots of the equation $ax^2 + bx + c = 0$ are $\alpha$ and $\beta$,then the value of $\alpha\beta^2 + \alpha^2\beta + \alpha\beta$ will be

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