If $\lambda $ $ \in $ R is such that the sum of the cubes of the roots of the equation, x2 + (2 $-$ $\lambda $) x + (10 $-$ $\lambda $) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :

Question

If $\lambda $ $ \in $ R is such that the sum of the cubes of the roots of the equation,
x² + (2 $-$ $\lambda $) x + (10 $-$ $\lambda $) = 0 is minimum, then the magnitude of the difference of the roots of this equation is :

$4\sqrt 2 $