If α and β are the roots of the equation 2x(2x+1)=1,then β is equal to

The given quadratic equation2x(2x+1)=1⇒ 4x2+2x−1=0 has roots α and βso,α+β=−12⇒2α+2β=−1and 4α2+2α−1=0From Eqs. (i) and (ii), we get4α2+2α+(2α+2β)=0⇒ 2α2+2α+β=0⇒β=−2α(α+1)