If α is a root of the equation 2x (2x + 1) = 1, then the other root, is

Let a, β be the roots of the equation 2x(2x+1)=1. Then, α+β=−12 and αβ=−14Again a is a root of 2x(2x+1)=0∴ 4α2+2α−1=0                                      ...(i)Now,α+β=−12⇒ β=−12−α⇒ β=−1+2α2⇒ β=−4α2+2α+2α2⇒ β=−2α(α+1)⇒ β=−2α2−2α⇒ β=−2α×α−2α⇒ β=α4α2−1−2α⇒ β=4α3−3α.