If α and β are the roots of the quadratic equation x 2 + x s i n θ - 2 s i n θ = 0 , θ ∈ 0 , π 2 , then α 12 + β 12 ( α - 12 + β - 12 ) . ( α - β ) 24 is equal to :

Step-by-step solution

Let E = α 12 + β 12 α - 12 + β - 12 α - β 24 = α 12 + β 12 α 12 + β 12 α 12 × β 12 α - β 24 E = α β 12 α - β 24 = α β 12 α + β 2 - 4 α β 12 Now α + β = - s i n θ α β = - 2 s i n θ ∴ E = - 2 s i n θ 12 - s i n θ 2 - 4 - 2 s i n θ 12 = 2 12 8 + s i n θ 12