The number of values of k for which the equation x3 − 3x + k = 0 has two different roots lying in the interval (0, 1) are

3 2 infinitely many no value of k satisfies the requirement

no value of k satisfies the requirement

Let $f(x)=x^3-3 x+k$. Let, if possible, a, b ∈ (0, 1) such that $f'(c)=0 \Rightarrow 3 c^2-3=0 \Rightarrow c= \pm 1$ ∴ no value of k satisfies the condition.