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

Step-by-step solution

Given equation is 2 x 2 x + 1 = 1 ⇒ 4 x 2 + 2 x - 1 = 0 .........(1) roots of equation 1 are α and β ∴ α + β = - 1 2 ⇒ β = - 1 2 - α ........(2) and 4 α 2 + 2 α - 1 = 0 ⇒ α 2 = 1 4 - α 2 .........(3) now - 2 α α + 1 = - 2 α 2 - 2 a = - 2 1 4 - α 2 - 2 α = - 1 2 - α = β