Number of integers in the range of 'c' so that the equation `x^3-3x+c=0` has all its roots real and distinct is

The value of k so that the equation x^(3)-12x+k=0 has distinct roots in [0,2] is

If the equation x^(3)-3ax^(2)+3bx-c=0 has positive and distinct roots, then

If the equation x^(3)-3ax^(2)+3bx-c=0 has positive and distinct roots, then

Show that the equation x^2+a x-4=0 has real and distinct roots for all real values of a .

Find the value of k for which the equation 3x^(2)-6x+k=0 has distinct and real root.

Show that the equation x^(2)+ax-4=0 has real and distinct roots for all real values of a .

Let f(x)=x^(2)-9-|x-a| . If the number of integers in the range of a so that f(x)=0 has 4 distinct real root is K ,then [(K)/(5)]= , ( [ .] denotes G.I.F)