If the sum of two roots of the equation x^3-7 | vedclass

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(B) Let the roots of the equation be $\alpha, \beta, \gamma$. Given $\alpha+\beta=0$.From the relation between roots and coefficients:$\alpha+\beta+\g

Vedclass · Accepted Answer

$5q=\frac{6r}{7p}$

Vedclass · Answer

(B) Let the roots of the equation be $\alpha, \beta, \gamma$. Given $\alpha+\beta=0$.From the relation between roots and coefficients:$\alpha+\beta+\gamma = 7p$Since $\alpha+\beta=0$,we have $\gamma=7p$.Also,$\alpha\beta+\beta\gamma+\gamma\alpha = 5q$$\alpha\beta + \gamma(\alpha+\beta) = 5q$$\alpha\beta + \gamma(0) = 5q \implies \alpha\beta = 5q$.Finally,$\alpha\beta\gamma = 6r$.Substituting the values of $\alpha\beta$ and $\gamma$:$(5q)(7p) = 6r$$35pq = 6r \implies 5q = \frac{6r}{7p}$.

If the sum of two roots of the equation $x^3-7px^2+5qx-6r=0$ is zero,then

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