If the sum of two roots of the equation x^3-2 | vedclass

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(A) Let the roots of the cubic equation be $\alpha, -\alpha,$ and $\beta$.From the relation between roots and coefficients:Sum of roots: $\alpha + (-\

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$\frac{3pq}{2}$

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(A) Let the roots of the cubic equation be $\alpha, -\alpha,$ and $\beta$.From the relation between roots and coefficients:Sum of roots: $\alpha + (-\alpha) + \beta = 2p \Rightarrow \beta = 2p$.Sum of roots taken two at a time: $\alpha(-\alpha) + (-\alpha)\beta + \alpha\beta = 3q$.$-\alpha^2 - \alpha\beta + \alpha\beta = 3q \Rightarrow -\alpha^2 = 3q$.Product of roots: $\alpha(-\alpha)\beta = 4r$.$-\alpha^2 \beta = 4r$.Substituting $\beta = 2p$ and $-\alpha^2 = 3q$ into the product equation:$(3q)(2p) = 4r$.$6pq = 4r$.$r = \frac{6pq}{4} = \frac{3pq}{2}$.

If the sum of two roots of the equation $x^3-2px^2+3qx-4r=0$ is zero,then the value of $r$ is

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