Find the equation at the tangent to $\displaystyle y = x^3 $ at the point $\displaystyle (t,t^3) $.

Hence deduce the values of k for which the equation $\displaystyle x^3 = kx -2 $ will have 3 real and distinct roots

The equation of the tangent is $\displaystyle y = 3t^2x - 2t^3$

what do I do next?

Thank you