Let $V=\{f(x) \in \mathbb{R}[x] \mid f(0)=0\},$ viewed as a real vector space. Consider the following assertions:
$\text{(I)}$ $V$ contains three linearly independent polynomials of degree $2$ .
$\text{(II)}$ $V$ contains two linearly independent polynomials of degree $3$.
Which of the following statements is correct?
- Both $\text{(I)}$ and $\text{(II)}$ are true.
- $\text{(I)}$ is true, but $\text{(II)}$ is false.
- $\text{(I)}$ is false, but $\text{(II)}$ is true.
- Neither $\text{(I)}$ nor $\text{(II)}$ is true.
