If the equation x3−3x+a=0 has distinct roots between  0 and 1, then the value of a is

Let f(x)=x3−3x+aIf f(x) has distinct roots between 0 and 1. Then, by Rolle's theorem f' (x) = 0 has a root between 0 and 1.  But , f′(x)=0⇒3x2−3=0⇒x=±1 Clearly, f'(x) = 0 does not have any root between 0 and 1. So, f (x) does not have distinct roots between 0 and 1 for any value of a.