Proof writing question: do I need to state the obvious, after showing the contradiction?

Question

Suppose $\lambda$ is a root of the polynomial $\mathscr{p}(x).$

Then it must be that "Q" follows, which is a contradiction.

Thus, $\lambda$ cannot be a root of $\mathscr{p}(x)$.

Do I have to state that last sentence? It sounds a bit redundant.

Or would my proof be a bit incomplete without it?

Thanks,