Question:
If $\alpha$ and $\beta$ are the roots of the equation $2 x(2 x+1)=1$, then $\beta$ is equal to :
Correct Option: , 3
Solution:
$\alpha$ and $\beta$ are the roots of the equation $4 x^{2}+2 x-1=0$.
$4 \alpha^{2}+2 \alpha=1 \Rightarrow \frac{1}{2}=2 \alpha^{2}+\alpha$ .........(1)
$\beta=\frac{-1}{2}-\alpha$
using equation (1)
$\beta=-\left(2 \alpha^{2}+\alpha\right)-\alpha$
$\beta=-2 \alpha^{2}-2 \alpha$
$\beta=-2 \alpha(\alpha+1)$
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