(b) infinite
A polynomial having zeroes 3 and 5 can be of the form $k(x-3)(x-5)$, where $k$ is any non-zero real constant. Since $k$ can take infinitely many values, infinitely many polynomials are possible.
The key idea is that zeroes fix only the ratio of coefficients, not the polynomial uniquely. Any scalar multiple $k \cdot p(x)$ has the same zeroes. Also, higher-degree polynomials (e.g., $k(x-3)(x-5)(x-1)$) can also have 3 and 5 as zeroes. So the answer is infinite, not "only one" or "exactly two."