If λ be the ratio of the roots of the quadratic equation in x , 3 m 2 x 2 + m m - 4 x + 2 = 0 , then the least value of m for which λ + 1 λ = 1 , is :

Step-by-step solution

Let α and β are the roots of given equation 3 m 2 x 2 + m m - 4 x + 2 = 0 . ∴ α + β = - m m - 4 3 m 2   &     α β = 2 3 m 2                   . . . . . . . . . i Given α β = λ         &       λ + 1 λ = 1 ⇒ α β + β α = 1 ⇒ α + β 2 = 3 α β Using equation i , we get - m m - 4 3 m 2 2 = 3 × 2 3 m 2 &#8