The seed has roots but are those roots deeply rooted in the heart so that we can say we have a root that prevents us from being unrooted? I think this language is not commonly used in English. In English we might just say there is no sincerity in himself, or no substance in himself, no conviction in himself, but I guess we can add ' has no root in himself'. The image of something driving deep into our heart, being rooted into us, is captured by the Greek phrase 'has a root in himself' based on the usage of the word 'root' in Palestine.
On the study of the word for root (ριζαν) used here, we get the key at what we are inquiring about.
Since the flora of Palestine is often threatened by heat or drought, special attention is directed to the root as the part of the plant which guarantees the existence of the whole. (TDNT, Kittel)
The idea is common in the Hebrew scriptures, for example:
No one can be established through wickedness, but the righteous cannot be uprooted. (NIV, Proverbs 12:3)
Literally the man who has a root in himself, is a man who posses a root of faith within himself. The idea indicates more than the seed having roots, for a seed in shallow soil has many roots but they do not root down deep. When the seed roots deep in a person, the person is sincerely connected to the roots within himself so become a possessor of the deeply rooted material. In this sense the idea of the root, or rooting of the roots, is transferred from the seed to the person himself. Either he has a root in himself, or he does not. Either he had deeply received the truth through sincere faith, having a root, or he just superficially believes some aspects of the thing on the surface. As soon as anything makes him decide between giving up something he loves for the sake of his faith, he tosses his faith and is uprooted in himself.