The cubic equation `x^3 - 6x^2 - 15x + k = 0` will have one real and two complex roots only if `k` satisfies :-

For what value of k the equation 2x^2-2kx+k=0 will have real and equal roots.

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.

For what values of k does the quadratic equation 4x^(2) - 12x - k =0 have no real roots ?

Prove that the equation 3x^(5)+15x -8=0 has only one real root .

Determine k and solve the equation 2x^3 - 6x^2 + 3x+k = 0 if one of its roots is twice the sum of the other two roots.