The equation in \(x\), \[3x^4 - 16x^3 +18x^2 + k = 0\] has four real solutions

- when \(-27 < k < 5\);
- when \(5< k <27\);
- when \(-27< k <-5\);
- when \(-5< k <0\).

The curve is the function \(y = 3x^4 - 16x^3 +18x^2 + k\).

The equation in \(x\), \[3x^4 - 16x^3 +18x^2 + k = 0\] has four real solutions

- when \(-27 < k < 5\);
- when \(5< k <27\);
- when \(-27< k <-5\);
- when \(-5< k <0\).

The curve is the function \(y = 3x^4 - 16x^3 +18x^2 + k\).