$ax^{3}+bx^{2}+cx+d$ is a polynomial on real $\text{x}$ over real coefficients $\text{a, b, c, d}$ wherein $a\neq 0.$ Which of the following statements is true?

1. $\text{d}$ can be chosen to ensure that $\text{x = 0}$ is a root for any given set $\text{a, b, c}$.
2. No choice of coefficient can make all roots identical.
3. $\text{a, b, c, d}$ can be chosen to ensure that all roots are complex.
4. $\text{c}$ alone cannot ensure that all roots are real.

Ans- A
150 points