Correct options are B) and C)
Given:2x(2x+1)=1i.e.4x
2
+2x−1=0
Let the other root be α,β
2α(2α+1)=1⇒
2
1
=α(2α+1)−(1)
⇒α+β=
4
−2
=−
2
1
β=−
2
1
−α
=−α(2α+1)−α
=−2α
2
−α−α
=−2α
2
−2α
=−2α
2
−2α=−2α(α+1)−(B)
=α(−2α−2)
α(4α
2
−3)[∵4α
2
+2α−1=0⇒−2α=4α
2
−1⇒−2α−2=4α
2
−3]
=4α
2
−3α→ Option -C
So, answer is B,C.