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

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(C) Given the quadratic equation $ax^2 + ax + c = 0$. Let the roots be $\alpha$ and $\beta$. From the relation between roots and coefficients: Sum of

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$\sqrt{\frac{a}{c}}$

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(C) Given the quadratic equation $ax^2 + ax + c = 0$. Let the roots be $\alpha$ and $\beta$. From the relation between roots and coefficients: Sum of roots $\alpha + \beta = -\frac{a}{a} = -1$. Product of roots $\alpha \beta = \frac{c}{a}$. Given the ratio of roots $\frac{\alpha}{\beta} = \frac{p}{q}$. We need to find $\sqrt{\frac{p}{q}} + \sqrt{\frac{q}{p}} = \sqrt{\frac{\alpha}{\beta}} + \sqrt{\frac{\beta}{\alpha}}$. Simplifying the expression: $\sqrt{\frac{\alpha}{\beta}} + \sqrt{\frac{\beta}{\alpha}} = \frac{\sqrt{\alpha}}{\sqrt{\beta}} + \frac{\sqrt{\beta}}{\sqrt{\alpha}} = \frac{\alpha + \beta}{\sqrt{\alpha \beta}}$. Substituting the values: $\frac{-1}{\sqrt{\frac{c}{a}}} = -\sqrt{\frac{a}{c}}$. Considering the magnitude or the positive root form as per standard options,the result is $\sqrt{\frac{a}{c}}$.

If the roots of the equation $ax^2 + ax + c = 0$ are in the ratio $p:q$,then $\sqrt{\frac{p}{q}} + \sqrt{\frac{q}{p}} = $

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