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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,we have $\alpha+\beta = -\frac{b}{

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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,we have $\alpha+\beta = -\frac{b}{a} = -\frac{2}{4} = -\frac{1}{2}$ and $\alpha\beta = \frac{c}{a} = -\frac{1}{4}$.From $\alpha+\beta = -\frac{1}{2}$,we get $\beta = -\frac{1}{2} - \alpha$.Since $\alpha$ is a root,it satisfies $4\alpha^{2}+2\alpha-1=0$,which implies $1 = 4\alpha^{2}+2\alpha$.Substituting $1 = 4\alpha^{2}+2\alpha$ into the expression for $\beta$:$\beta = -\frac{4\alpha^{2}+2\alpha}{2} - \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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