How many quadratic polynomials with real coefficients are there such that the set of roots equals the set of non-zero coefficients? (For clarification: If the polynomial is $a{x}^2+bx+c$, $a\ne 0$, and the roots are $r$ and $s$, then the requirement is that $\{r,s\}=\{x\in \{a,b,c\}\mid x\ne 0\}$.)