If the sum of the roots of the equation {x^2} | vedclass

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(C) Let the roots of the quadratic equation ${x^2} + px + q = 0$ be $\alpha$ and $\beta$.From the properties of quadratic equations,the sum of the roo

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${p^2} + p = 2q$

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(C) Let the roots of the quadratic equation ${x^2} + px + q = 0$ be $\alpha$ and $\beta$.From the properties of quadratic equations,the sum of the roots is $\alpha + \beta = -p$ and the product of the roots is $\alpha \beta = q$.According to the problem,the sum of the roots is equal to the sum of their squares:$\alpha + \beta = {\alpha ^2} + {\beta ^2}$We know that ${\alpha ^2} + {\beta ^2} = {(\alpha + \beta )^2} - 2\alpha \beta$.Substituting the values of the sum and product of the roots into the equation:$-p = {(-p)^2} - 2q$$-p = {p^2} - 2q$Rearranging the terms,we get:${p^2} + p = 2q$.

If the sum of the roots of the equation ${x^2} + px + q = 0$ is equal to the sum of their squares,then

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