Official solution
\[\alpha \] and
\[\beta \] are the roots of the equation
4x2 + 2x -- 1 = 0.
\[ \therefore \] \[\alpha \] + \[\beta \] = \[ - {1 \over 2}\]
\[ \Rightarrow \] -1 = 2\[\alpha \] + 2\[\beta \]
and 4\[\alpha \]2 + 2\[\alpha \] - 1 = 0
\[ \Rightarrow \] 4\[\alpha \]2 + 2\[\alpha \] + 2\[\alpha \] + 2\[\beta \] = 0
\[ \Rightarrow \] \[\beta \] = \[ - 2\alpha \left( {\alpha + 1} \right)\]