If the equation `x^(3) - 3x + a = 0` has distinct roots between 0 and 1, then the value of a is

Statement-1: There is a value of k for which the equation x^(3) - 3x + k = 0 has a root between 0 and 1. Statement-2: Between any two real roots of a polynomial there is a root of its derivation.

Statement-1: There is a value of k for which the equation x^(3) - 3x + k = 0 has a root between 0 and 1. Statement-2: Between any two real roots of a polynomial there is a root of its derivation.

The number of values of 'k' for which the equation x^(2) - 3x + k = 0 has two distinct roots lying in the interval (0,1) is :

If the equation 2x^(3) -6x + k=0 has three real and distinct roots, then find the value (s) of k.

If the equation 2x^(3) -6x + k=0 has three real and distinct roots, then find the value (s) of k.

Statement-1 : There is no value ofb k for which the equaiton x^(3)-3x+k=0 has two distinct roots between 0 and 1 . Statement-2: x gt sin x "for all" x gt0