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

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(A) For the quadratic equation $ax^2 + bx + c = 0$,the sum and product of roots are given by:$\alpha + \beta = -\frac{b}{a}$ and $\alpha\beta = \frac{

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

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(A) For the quadratic equation $ax^2 + bx + c = 0$,the sum and product of roots are given by:$\alpha + \beta = -\frac{b}{a}$ and $\alpha\beta = \frac{c}{a}$.We need to find the value of $\alpha\beta^2 + \alpha^2\beta + \alpha\beta$.Factor out $\alpha\beta$ from the expression:$\alpha\beta^2 + \alpha^2\beta + \alpha\beta = \alpha\beta(\beta + \alpha + 1)$.Substitute the values of $(\alpha + \beta)$ and $(\alpha\beta)$:$= \left(\frac{c}{a}\right) \left(-\frac{b}{a} + 1\right)$$= \left(\frac{c}{a}\right) \left(\frac{a - b}{a}\right)$$= \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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