Why these polynomials p_1, p_2, p_3, p_4 doesn't span space of degree 2 polynomial?

We know the definition of span:

If is a set of vectors in a vector space , then the subspace of consisting of all linear combinations of the vectors in is called the space spanned by , and we say that the vectors span . To indicate that is the space spanned by the vectors in the set , we write:

or

I've a math problem and asked to find out whether the polynomials span a space or not. Determine whether the following polynomials span (the set of degree 2 polynomials).

The book says it doesn't span

How do they figure out that subspace does not consist of all linear combination of polynomials ? How does one come to this conclusion?