If alpha and beta are the roots of the equati | vedclass

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(C) The given equation is $2x(2x + 1) = 1$,which simplifies to $4x^{2} + 2x - 1 = 0$.Since $\alpha$ and $\beta$ are the roots of this quadratic equati

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$-2\alpha(\alpha + 1)$

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(C) The given equation is $2x(2x + 1) = 1$,which simplifies to $4x^{2} + 2x - 1 = 0$.Since $\alpha$ and $\beta$ are the roots of this quadratic equation,the sum of the roots is $\alpha + \beta = -b/a = -2/4 = -1/2$.From this,we can express $\beta$ as $\beta = -1/2 - \alpha$.Also,since $\alpha$ is a root,it satisfies the equation $4\alpha^{2} + 2\alpha - 1 = 0$,which implies $4\alpha^{2} + 2\alpha = 1$,or $2\alpha^{2} + \alpha = 1/2$.Substituting $1/2 = 2\alpha^{2} + \alpha$ into the expression for $\beta$:$\beta = -(2\alpha^{2} + \alpha) - \alpha$.$\beta = -2\alpha^{2} - \alpha - \alpha$.$\beta = -2\alpha^{2} - 2\alpha$.$\beta = -2\alpha(\alpha + 1)$.

If $\alpha$ and $\beta$ are the roots of the equation $2x(2x + 1) = 1$,then $\beta$ is equal to

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