The value of a for which the sum of cubes of the roots of the equation, x 2 - a x + 2 a - 3 = 0   ∀ a ∈ 1 2 , 4 attains its minimum value is

Step-by-step solution

Let a , β be the roots, Then, α 3 + β 3 = α + β 3 - 3 α β α + β = a 3 - 3 2 a - 3 a = a 3 - 6 a 2 + 9 a = E ( s a y ) ∴ d E d a = 3 a 2 - 12 a + 9 = 3 a - 1 a - 3 Thus, E attains its minimum value at ‘ a ’ = 3