Chromatic polynomials closed

Question

Check which of the following can be chromatic polynomials of a non-null graph ?

i) x⁵ - 4x³ - 2x² + x + 4

ii) x⁶ - 3x⁵ + 2x⁴ - 1

P.S I know for a non-null graph G, X(G) (i.e. chromatic number) is at least 2. How to proceed further ??

Comments

Let me add what I feel is the way to approach such a problem for the sake of completeness. (Others may not follow what exactly it was that you understood.)

A chromatic polynomial P(G,x) for a Graph G represents the number of ways of properly coloring a graph using x or less colors.
So if you plug in the value of x = 1, a valid polynomial should tell you the number of ways in which you could properly color a graph using exactly 1 color. But you cannot properly color any non-null graph with less than 2 colors. Therefore the polynomial should tell you that there are 0 ways of doing so.

Therefore, only the first polynomial is valid.

Note: As per my understanding, any chromatic polynomial (null-graph or not) that generates a negative value for any positive integral value of x should be invalid. (How can there be -1 ways of coloring a graph?)