Question

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

• A. $2\alpha (\alpha -1)$
  
• B. $-2\alpha (\alpha +1)$
  
• C. $2{\alpha }^2$
  
• D. $2\alpha (\alpha +1)$
  

Answer 1

The correct option is B $-2\alpha (\alpha +1)$


$2x(2x+1)=1$
If $\alpha$ & $\beta$ are the roots $i.e\alpha$ & $\beta$ satisfy this equation
$2\alpha (2\alpha +1)=1\Rightarrow \alpha (2\alpha +1)=\frac{1}{2}$
$4x^2+2x-1=0$
$\alpha +\beta =\frac{-1}{2}=-\alpha (2\alpha +1)$
$\beta =-\alpha (2\alpha +1)-\alpha =-\alpha (2\alpha +2)=-2\alpha (\alpha +1)$