KVPY 2019 SA Exam Previous Papers

Let $\mathit{p}\left(\mathit{x}\right)={\mathit{x}}^2+\mathit{a}\mathit{x}+\mathit{b}$ have two distinct real roots, where a, b are real numbers. Define g(x) = $\mathit{p}\left({\mathit{x}}^3\right)$ for all real number x. Then which of the following statements are true ?
I. g has exactly two distinct real roots
II. g can have more than two distinct real roots
III. There exists a real number a such that g(x) ≥ α for all real x