Answer
False.
Work Step by Step
The zero of a polynomial is when $f(x)=0$. Take the polynomial $p(x)=1+x$. To find the roots, use $p(x)=0$ to get $$0=1+x \implies x=-1$$ Therefore, the root is at $x=-1$, contrary to the statement ($p(0)=1$). Thus, the statement is false.
