finding value of constant such that function has distinct root

Question

we have the function cubic function $$ x^3 -12x +k =0 $$ it has distinct root in $$ [0,2{]} $$ that task given to us is to find the the value of k satisfying the above conditions I proceeded differentiated the function and by equating differential coefficient to zero i found that function turned at x=2 now if the function turned turned at least once then it must be having least of 1 root now how will we use this result to find value of the constant k

Answer 1

Between any two distinct roots of the function, there is a root of the derivative. But the derivative is $0$ only at $\pm 2$. Thus there cannot be such a $k$.