Suppose that a quadratic polynomial $x^2+bx+1 \in R$,has two zeroes which are both real then which one of the following is necessarily true?

Question

$\begin{array}{1 1}\text{b can have infinitely many values}\\\text{b has a unique value}\\\text{b has at most two distinct values}\\\text{b has at most four distinct values}\end{array}$