Question:
If $\alpha$ and $\beta$ are the roots of the equation $2 x(2 x+1)=1$, then $\beta$ is equal to:
Correct Option: , 2
Solution:
(2) Let $\alpha$ and $\beta$ be the roots of the given quadratic equation,
$2 x^{2} \cdot 2 x-1=0$...(i)
Then, $\alpha+\beta=-\frac{1}{2} \Rightarrow-1=2 \alpha+2 \beta$
and $4 \alpha^{2}+2 \alpha-1=0$ $[\because \alpha$ is root of eq. (i) $]$
$\Rightarrow 4 \alpha^{2}+2 \alpha+2 \alpha+2 \beta=0 \Rightarrow \beta=-2 \alpha(\alpha+1)$