Is it possible for a cubic equation to have three imaginary solutions?

Yes, a cubic equation can have three imaginary solutions, but this occurs only when all the roots are complex. For a cubic equation with real coefficients, if it has one real root, the other two roots must be complex conjugates, resulting in one real and two imaginary solutions. However, if the cubic has no real roots, it can have three distinct complex roots, all of which would be imaginary.