Certain Properties about Weierstrass polynomials

Question

In my Real Analysis class we learned about the Stone-Weierstrass Theorem, which is more common known as the Weierstrass Approximation theorem saying that you can approximate anything continuous on the interval(or you can extend it to a general Topological space) with a sequence of polynomials, $(p_n)$ that goes to the function uniformly. So my question is this: Are all the terms in the sequence of $(p_n)$ is 0 when evaluated at 0? If yes, what is a way to prove it? Thanks